Attachment #39033 for bug #62982

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@DOCSTRING(sin)
@DOCSTRING(cos)
@DOCSTRING(tan)
@DOCSTRING(cot)
@DOCSTRING(sec)
@DOCSTRING(csc)
@DOCSTRING(cot)

@DOCSTRING(asin)
@DOCSTRING(acos)
@DOCSTRING(atan)
@DOCSTRING(acot)
@DOCSTRING(asec)
@DOCSTRING(acsc)
@DOCSTRING(acot)

@DOCSTRING(sinh)
@DOCSTRING(cosh)
@DOCSTRING(tanh)
@DOCSTRING(coth)
@DOCSTRING(sech)
@DOCSTRING(csch)
@DOCSTRING(coth)

@DOCSTRING(asinh)
@DOCSTRING(acosh)
@DOCSTRING(atanh)
@DOCSTRING(acoth)
@DOCSTRING(asech)
@DOCSTRING(acsch)
@DOCSTRING(acoth)

Each of these functions expect a single argument.  For matrix arguments,
they work on an element by element basis.  For example,




@node Control Theory
@chapter Control Theory

The Octave Control Systems Toolbox (@acronym{OCST}) was initially developed
by Dr.@: A. Scottedward Hodel 
@email{a.s.hodel@@eng.auburn.edu} with the assistance
of his students

@item John E. Ingram @email{John.Ingram@@sea.siemans.com}, and 
@item Kristi McGowan.  
@end itemize
This development was supported in part by @acronym{NASA}'s Marshall Space Flight 
Center as part of an in-house @acronym{CACSD} environment.  Additional important 
contributions were made by Dr. Kai Mueller @email{mueller@@ifr.ing.tu-bs.de}
and Jose Daniel Munoz Frias (@code{place.m}).

An on-line menu-driven tutorial is available via @code{DEMOcontrol};
beginning @acronym{OCST} users should start with this program. 

@DOCSTRING(DEMOcontrol)


* sysstructss::                 
@end menu

The @acronym{OCST} stores all dynamic systems in
a single data structure format that can represent continuous systems,
discrete-systems, and mixed (hybrid) systems in state-space form, and
can also represent purely continuous/discrete systems in either
transfer function or pole-zero form. In order to
provide more flexibility in treatment of discrete/hybrid systems, the
@acronym{OCST} also keeps a record of which system outputs are sampled.

Octave structures are accessed with a syntax much like that used
by the C programming language.  For consistency in
use of the data structure used in the @acronym{OCST}, it is recommended that
the system structure access m-files be used (@pxref{sysinterface}).
Some elements of the data structure are absent depending on the internal
system representation(s) used.  More than one system representation
can be used for @acronym{SISO} systems; the @acronym{OCST} m-files ensure that all representations
used are consistent with one another.

@DOCSTRING(sysrepdemo)

@node sysstructvars
@subsection Variables common to all @acronym{OCST} system formats

The data structure elements (and variable types) common to all  system
representations are listed below; examples of the initialization

@node sysinterface
@section System Construction and Interface Functions

Construction and manipulations of the @acronym{OCST} system data structure
(@pxref{sysstruct}) requires attention to many details in order
to ensure that data structure contents remain consistent.  Users
are strongly encouraged to use the system interface functions


@DOCSTRING(zgshsr)

@strong{References}
@table @strong
@item  ZGEP
 Hodel, @cite{Computation of Zeros with Balancing}, 1992, Linear Algebra
 and its Applications
@item @strong{Generalized CG}
 Golub and Van Loan, @cite{Matrix Computations, 2nd ed} 1989.
@end table

@node sysprop




@noindent
and select the first row of the matrix.

@c FIXED -- sections on variable prefer_zero_one_indexing were removed
vector.  If the indices are vectors made up of only ones and zeros, the
result is a new matrix whose elements correspond to the elements of the
index vector that are equal to one.  For example,

Indexing a scalar with a vector of ones can be used to create a
@group
a = [1, 2; 3, 4];
a ([1, 0], :)
@end group
@end example

@noindent
selects the first row of the matrix @code{a}.

This operation can be useful for selecting elements of a matrix based on
some condition, since the comparison operators return matrices of ones
and zeros.

This special zero-one form of indexing leads to a conflict with the
standard indexing operation.  For example, should the following
statements

@example
@group
a = [1, 2; 3, 4];
a ([1, 1], :)
@end group
@end example

@noindent
return the original matrix, or the matrix formed by selecting the first
row twice?  Although this conflict is not likely to arise very often in
practice, you may select the behavior you prefer by setting the built-in
variable @code{prefer_zero_one_indexing}.

@c XXX FIXME XXX -- this variable no longer exists!

@defvr {Built-in Variable} prefer_zero_one_indexing
If the value of @code{prefer_zero_one_indexing} is nonzero, Octave
will perform zero-one style indexing when there is a conflict with the
normal indexing rules.  @xref{Index Expressions}.  For example, given a
matrix

@example
a = [1, 2, 3, 4]
@end example

@noindent
with @code{prefer_zero_one_indexing} is set to nonzero, the
expression

@example
a ([1, 1, 1, 1])
@end example

@noindent
results in the matrix @code{[ 1, 2, 3, 4 ]}.  If the value of
@code{prefer_zero_one_indexing} set to 0, the result would be
the matrix @code{[ 1, 1, 1, 1 ]}.

In the first case, Octave is selecting each element corresponding to a
@samp{1} in the index vector.  In the second, Octave is selecting the
first element multiple times.

The default value for @code{prefer_zero_one_indexing} is 0.
@end defvr

Finally, indexing a scalar with a vector of ones can be used to create a
vector the same size as the index vector, with each element equal to
the value of the original scalar.  For example, the following statements


@end example

@noindent
deletes the first, second, and fifth columns.

An assignment is an expression, so it has a value.  Thus, @code{z = 1}
as an expression has the value 1.  One consequence of this is that you





@defvr {Keyword} return
When Octave encounters the keyword @code{return} inside a function or
script, it returns control to the caller immediately. At the top level,
the return statement is ignored.  A @code{return} statement is assumed
at the end of every function definition.
@end defvr


@example
@group
ColumnVector dx (3);

dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
                 - 8.375e-06*pow (x(0), 2));


@end example

@noindent
define the right-hand side of the differential equation.  Finally, we
can return @code{dx}:

@example

Lines 124-130 read from disk files in various formats. Link Here

(-)octave-2.1.58/doc/interpreter/io.txi (-1 / +1 lines)
124	written by the @code{save} command can be controlled using the built-in	124	written by the @code{save} command can be controlled using the built-in
125	variables @code{default_save_format} and @code{save_precision}.	125	variables @code{default_save_format} and @code{save_precision}.
126		126
127	Note that Octave can not yet save or load structure variables or any	127	Note that Octave cannot yet save or load structure variables or any
128	user-defined types.	128	user-defined types.
129		129
130	@DOCSTRING(save)	130	@DOCSTRING(save)

Lines 44-50 The optional item @var{ranges} has the s Link Here

(-)octave-2.1.58/doc/interpreter/plot.txi (-1 / +1 lines)
44		44
45	@noindent	45	@noindent
46	and may be used to specify the ranges for the axes of the plot,	46	and may be used to specify the ranges for the axes of the plot,
47	independent of the actual range of the data. The range for the y axes	47	independent of the actual range of the data. The range for the y axis
48	and any of the individual limits may be omitted. A range @code{[:]}	48	and any of the individual limits may be omitted. A range @code{[:]}
49	indicates that the default limits should be used. This normally means	49	indicates that the default limits should be used. This normally means
50	that a range just large enough to include all the data points will be	50	that a range just large enough to include all the data points will be

Lines 103-109 a = Link Here

(-)octave-2.1.58/doc/interpreter/struct.txi (-1 / +4 lines)
103	@{	103	@{
104	b =	104	b =
105	@{	105	@{
106	c = <structure>	106	c =
		107	@{
		108	d: 1x1 struct
		109	@}
107	@}	110	@}
108	@}	111	@}
109	@end group	112	@end group




    k=0;
    while(k > 8 || k < 1)
      k = menu("Octave State Space Analysis Demo", ...
        "System gramians (gram, dgram)", ...
        "System zeros (tzero)", ...
        "Continuous => Discrete and Discrete => Continuous conversions (c2d,d2c)", ...
        "Algebraic Riccati Equation (are, dare)", ...

      prompt

      clc
      disp("System Gramians: (see Moore, IEEE T-AC, 1981) \n");
      disp("Example #1, consider the discrete time state space system:\n");
      a=[1, 5, -8.4; 1.2, -3, 5; 1, 7, 9]
      b=[1, 5; 2, 6; -4.4, 5]
      c=[1, -1.5, 2; 6, -9.8, 1]
      d=0
      prompt
      disp("\nThe discrete controllability gramian is computed as follows:");
      cmd = "gramian = dgram(a, b);";
      run_cmd;
      disp("Results:\n");
      gramian = dgram(a,b)
      disp("Variable Description:\n");
      disp("gramian => discrete controllability gramian");
      disp("a, b => a and b matrices of discrete time system\n");
      disp("A dual approach may be used to compute the observability gramian.");
      prompt
      clc


      c=[1, -1.1, 7; 3, -9.8, 2]
      d=0
      prompt
      disp("\nThe continuous controllability gramian is computed as follows:");
      cmd = "gramian = gram(a, b);";
      run_cmd;
      disp("Results:\n");
      gramian = gram(a,b)
      disp("Variable Description:\n");
      disp("gramian => continuous controllability gramian");
      disp("a, b => a and b matrices of continuous time system\n");
      disp("A dual approach may be used to compute the observability gramian.");
      prompt
      clc





## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{x} =} are (@var{a}, @var{b}, @var{c}, @var{opt})
## Solve the Algebraic Riccati Equation
## @iftex
## @tex
## $$
## A^{ \rm T }\,X + X\,A - X\,B\,X + C = 0
## $$
## @end tex
## @end iftex

## for identically dimensioned square matrices
## @table @var
## @item a
## @var{n} by @var{n} matrix;
## @item b
##   @var{n} by @var{n} matrix or @var{n} by @var{m} matrix; in the latter case
##   @var{b} is replaced by @math{b:=b*b'};
## @item c
##   @var{n} by @var{n} matrix or @var{p} by @var{m} matrix; in the latter case
##   @var{c} is replaced by @math{c:=c'*c};
## @item opt
## (optional argument; default = @code{"B"}):
## String option passed to @code{balance} prior to ordered Schur decomposition.
## @end table
##
## @strong{Output}
## @table @var
## @item x
## solution of the @acronym{ARE}.
## @end table
##
## @strong{Method}
## Laub's Schur method (@acronym{IEEE} Transactions on
## Automatic Control, 1979) is applied to the appropriate Hamiltonian
## matrix.
##

Lines 18-24 Link Here

(-)octave-2.1.58/scripts/control/base/bddemo.m (-1 / +1 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} bddemo (@var{inputs})	20	## @deftypefn {Function File} {} bddemo (@var{inputs})
21	## Octave Controls toolbox demo: Block Diagram Manipulations demo	21	## Octave Controls toolbox demo: Block Diagram Manipulations demo.
22	## @end deftypefn	22	## @end deftypefn
23		23
24	## Author: David Clem	24	## Author: David Clem




## @deftypefn {Function File} {[@var{wmin}, @var{wmax}] =} bode_bounds (@var{zer}, @var{pol}, @var{dflg}, @var{tsam})
## Get default range of frequencies based on cutoff frequencies of system
## poles and zeros.
## Frequency range is the interval
## @iftex
## @tex
## $ [ 10^{w_{min}},~10^{w_{max}} ] $
## @end tex
## @end iftex
## @ifinfo
## [10^@var{wmin}, 10^@var{wmax}]
## @end ifinfo
##
## Used internally in @command{__freqresp__} (@command{bode}, @command{nyquist})
## @end deftypefn

function [wmin, wmax] = bode_bounds (zer, pol, DIGITAL, tsam)

Lines 39-45 Link Here

(-)octave-2.1.58/scripts/control/base/bode.m (-2 / +2 lines)
39	## @end itemize	39	## @end itemize
40	##	40	##
41	## @strong{Default} the default frequency range is selected as follows: (These	41	## @strong{Default} the default frequency range is selected as follows: (These
42	## steps are NOT performed if @var{w} is specified)	42	## steps are @strong{not} performed if @var{w} is specified)
43	## @enumerate	43	## @enumerate
44	## @item via routine __bodquist__, isolate all poles and zeros away from	44	## @item via routine __bodquist__, isolate all poles and zeros away from
45	## @var{w}=0 (@var{jw}=0 or @math{@code{exp}(jwT)}=1) and select the frequency	45	## @var{w}=0 (@var{jw}=0 or @math{@code{exp}(jwT)}=1) and select the frequency
Lines 91-97 Link Here
91	## Failure to include a concluding semicolon will yield some garbage	91	## Failure to include a concluding semicolon will yield some garbage
92	## being printed to the screen (@code{ans = []}).	92	## being printed to the screen (@code{ans = []}).
93	##	93	##
94	## @item If the requested plot is for an MIMO system, mag is set to	94	## @item If the requested plot is for an @acronym{MIMO} system, mag is set to
95	## @math{\|\|G(jw)\|\|} or @math{\|\|G(@code{exp}(jwT))\|\|}	95	## @math{\|\|G(jw)\|\|} or @math{\|\|G(@code{exp}(jwT))\|\|}
96	## and phase information is not computed.	96	## and phase information is not computed.
97	## @end enumerate	97	## @end enumerate

Lines 18-24 Link Here

(-)octave-2.1.58/scripts/control/base/__bodquist__.m (-2 / +2 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{f}, @var{w}, @var{rsys}] =} __bodquist__ (@var{sys}, @var{w}, @var{out_idx}, @var{in_idx})	20	## @deftypefn {Function File} {[@var{f}, @var{w}, @var{rsys}] =} __bodquist__ (@var{sys}, @var{w}, @var{out_idx}, @var{in_idx})
21	## used internally by bode, nyquist; compute system frequency response.	21	## Used internally by @command{bode}, @command{nyquist}; compute system frequency response.
22	##	22	##
23	## @strong{Inputs}	23	## @strong{Inputs}
24	## @table @var	24	## @table @var
Lines 45-51 Link Here
45	## @code{bode}, @code{nichols}, and @code{nyquist} share the same	45	## @code{bode}, @code{nichols}, and @code{nyquist} share the same
46	## introduction, so the common parts are	46	## introduction, so the common parts are
47	## in __bodquist__. It contains the part that finds the number of arguments,	47	## in __bodquist__. It contains the part that finds the number of arguments,
48	## determines whether or not the system is SISO, and computes the frequency	48	## determines whether or not the system is @acronym{SISO}, and computes the frequency
49	## response. Only the way the response is plotted is different between the	49	## response. Only the way the response is plotted is different between the
50	## these functions.	50	## these functions.
51	## @end deftypefn	51	## @end deftypefn

Lines 18-24 Link Here

(-)octave-2.1.58/scripts/control/base/controldemo.m (-1 / +1 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} controldemo ()	20	## @deftypefn {Function File} {} controldemo ()
21	## Controls toolbox demo.	21	## Control Systems Toolbox demo.
22	## @end deftypefn	22	## @end deftypefn
23	## @seealso{Demo programs: bddemo, frdemo, analdemo, moddmeo, rldemo}	23	## @seealso{Demo programs: bddemo, frdemo, analdemo, moddmeo, rldemo}
24		24




## -*- texinfo -*-
## @deftypefn {Function File} {} ctrb (@var{sys}, @var{b})
## @deftypefnx {Function File} {} ctrb (@var{a}, @var{b})
## Build controllability matrix:
## @iftex
## @tex
## $$ Q_s = [ ~ B ~ A\,B ~ A^2B ~ \ldots ~ A^{n-1}B ~ ] $$
## @end tex
## @end iftex
## @ifinfo
## @example
##              2       n-1
## Qs = [ B AB A B ... A   B ]
## @end example
## @end ifinfo
##
## of a system data structure or the pair (@var{a}, @var{b}).
##
## @command{ctrb} forms the controllability matrix.
## The numerical properties of @command{is_controllable}
## are much better for controllability tests.
## @end deftypefn


Lines 19-25 Link Here

(-)octave-2.1.58/scripts/control/base/damp.m (-1 / +1 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} damp (@var{p}, @var{tsam})	20	## @deftypefn {Function File} {} damp (@var{p}, @var{tsam})
21	## Displays eigenvalues, natural frequencies and damping ratios	21	## Displays eigenvalues, natural frequencies and damping ratios
22	## of the eigenvalues of a matrix @var{p} or the @math{A}-matrix of a	22	## of the eigenvalues of a matrix @var{p} or the @math{A} matrix of a
23	## system @var{p}, respectively.	23	## system @var{p}, respectively.
24	## If @var{p} is a system, @var{tsam} must not be specified.	24	## If @var{p} is a system, @var{tsam} must not be specified.
25	## If @var{p} is a matrix and @var{tsam} is specified, eigenvalues	25	## If @var{p} is a matrix and @var{tsam} is specified, eigenvalues




## 02111-1307, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{x} =} dare (@var{a}, @var{b}, @var{q}, @var{r}, @var{opt})
##
## Return the solution, @var{x} of the discrete-time algebraic Riccati
## equation
## @iftex
## @tex
## $$
## A^{ \rm T }XA - X + A^{ \rm T }XB \, (R + B^{ \rm T }XB)^{-1} B^{ \rm T }XA + Q = 0
## $$
## @end tex
## @end iftex

## @strong{Inputs}
## @table @var
## @item a
## @var{n} by @var{n} matrix;
##
## @item b
## @var{n} by @var{m} matrix;
##
## @item q
## @var{n} by @var{n} matrix, symmetric positive semidefinite, or a @var{p} by @var{n} matrix,
## In the latter case @math{q:=q'*q} is used;
##
## @item r
## @var{m} by @var{m}, symmetric positive definite (invertible);
##
## @item opt
## (optional argument; default = @code{"B"}):
## String option passed to @code{balance} prior to ordered @var{QZ} decomposition.
## @end table
##
## @strong{Output}
## @table @var
## @item x
## solution of @acronym{DARE}.
## @end table
##
## @strong{Method}
## Generalized eigenvalue approach (Van Dooren; @acronym{SIAM} J.
##  Sci. Stat. Comput., Vol 2) applied  to the appropriate symplectic pencil.
##
##  See also: Ran and Rodman, @cite{Stable Hermitian Solutions of Discrete
##  Algebraic Riccati Equations}, Mathematics of Control, Signals and
##  Systems, Vol 5, no 2 (1992), pp 165--194.
##
## @end deftypefn
## @seealso{balance and are}

Lines 21-27 Link Here

(-)octave-2.1.58/scripts/control/base/dcgain.m (-1 / +1 lines)
21	## Returns dc-gain matrix. If dc-gain is infinite	21	## Returns dc-gain matrix. If dc-gain is infinite
22	## an empty matrix is returned.	22	## an empty matrix is returned.
23	## The argument @var{tol} is an optional tolerance for the condition	23	## The argument @var{tol} is an optional tolerance for the condition
24	## number of the @math{A}-Matrix in @var{sys} (default @var{tol} = 1.0e-10)	24	## number of the @math{A} Matrix in @var{sys} (default @var{tol} = 1.0e-10)
25	## @end deftypefn	25	## @end deftypefn
26		26
27	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>	27	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>




## -*- texinfo -*-
## @deftypefn {Function File} {} DEMOcontrol
## Octave Control Systems Toolbox demo/tutorial program.  The demo
## allows the user to select among several categories of @acronym{OCST} function:
## @example
## @group
## octave:1> DEMOcontrol

## @end group
## @end example
## Command examples are interactively run for users to observe the use
## of @acronym{OCST} functions.
## @end deftypefn
## @seealso{Demo Programs: bddemo.m, frdemo.m, analdemo.m,
## moddmeo.m, rldemo.m}


function DEMOcontrol ()

  puts ("O C T A V E    C O N T R O L   S Y S T E M S   T O O L B O X");

  while (1)


Lines 18-28 Link Here

(-)octave-2.1.58/scripts/control/base/dgram.m (-3 / +21 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} dgram (@var{a}, @var{b})	20	## @deftypefn {Function File} {} dgram (@var{a}, @var{b})
21	## Return controllability grammian of discrete time system	21	## Return controllability gramian of discrete time system
		22	## @iftex
		23	## @tex
		24	## $$ x_{k+1} = a\,x_k + b\,u_k $$
		25	## @end tex
		26	## @end iftex
		27	## @ifinfo
22	## @example	28	## @example
23	## x(k+1) = a x(k) + b u(k)	29	## x(k+1) = a x(k) + b u(k)
24	## @end example	30	## @end example
25	##	31	## @end ifinfo
		32	##
26	## @strong{Inputs}	33	## @strong{Inputs}
27	## @table @var	34	## @table @var
28	## @item a	35	## @item a
Lines 31-41 Link Here
31	## @var{n} by @var{m} matrix	38	## @var{n} by @var{m} matrix
32	## @end table	39	## @end table
33	##	40	##
34	## @strong{Outputs}	41	## @strong{Output}
		42	## @table @var
		43	## @item m
		44	## @var{n} by @var{n} matrix, satisfies
		45	## @iftex
		46	## @tex
		47	## $$ a\,m\,a^{ \rm T } - m + b\,b^{ \rm T } = 0 $$
		48	## @end tex
		49	## @end iftex
		50	## @ifinfo
35	## @var{m} (@var{n} by @var{n}) satisfies	51	## @var{m} (@var{n} by @var{n}) satisfies
36	## @example	52	## @example
37	## a m a' - m + b*b' = 0	53	## a m a' - m + b*b' = 0
38	## @end example	54	## @end example
		55	## @end ifinfo
		56	## @end table
39	## @end deftypefn	57	## @end deftypefn
40		58
41	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	59	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 37-43 Link Here

(-)octave-2.1.58/scripts/control/base/dlqr.m (-2 / +2 lines)
37	## @iftex	37	## @iftex
38	## @tex	38	## @tex
39	## $$	39	## $$
40	## J = \sum x^T Q x + u^T R u	40	## J = \sum x^{ \rm T } Q x + u^{ \rm T } R u
41	## $$	41	## $$
42	## @end tex	42	## @end tex
43	## @end iftex	43	## @end iftex
Lines 53-59 Link Here
53	## @iftex	53	## @iftex
54	## @tex	54	## @tex
55	## $$	55	## $$
56	## J = \sum x^T Q x + u^T R u + 2 x^T Z u	56	## J = \sum x^{ \rm T } Q x + u^{ \rm T } R u + 2 x^{ \rm T } Z u
57	## $$	57	## $$
58	## @end tex	58	## @end tex
59	## @end iftex	59	## @end iftex

Lines 23-47 Link Here

(-)octave-2.1.58/scripts/control/base/dlyap.m (-5 / +31 lines)
23	## @strong{Inputs}	23	## @strong{Inputs}
24	## @table @var	24	## @table @var
25	## @item a	25	## @item a
26	## @var{n} by @var{n} matrix	26	## @var{n} by @var{n} matrix;
27	## @item b	27	## @item b
28	## Matrix: @var{n} by @var{n}, @var{n} by @var{m}, or @var{p} by @var{n}.	28	## Matrix: @var{n} by @var{n}, @var{n} by @var{m}, or @var{p} by @var{n}.
29	## @end table	29	## @end table
30	##	30	##
31	## @strong{Outputs}	31	## @strong{Output}
32	## @var{x}: matrix satisfying appropriate discrete time Lyapunov equation.	32	## @table @var
		33	## @item x
		34	## matrix satisfying appropriate discrete time Lyapunov equation.
		35	## @end table
		36	##
33	## Options:	37	## Options:
34	## @itemize @bullet	38	## @itemize @bullet
35	## @item @var{b} is square: solve @code{a x a' - x + b = 0}	39	## @item @var{b} is square: solve
		40	## @iftex
		41	## @tex
		42	## $$ a\,x\,a^{ \rm T } - x + b = 0 $$
		43	## @end tex
		44	## @end iftex
		45	## @ifinfo
		46	## @code{a x a' - x + b = 0}
		47	## @end ifinfo
36	## @item @var{b} is not square: @var{x} satisfies either	48	## @item @var{b} is not square: @var{x} satisfies either
		49	## @iftex
		50	## @tex
		51	## $$ a\,x\,a^{ \rm T } - x + b\,b^{ \rm T } = 0 $$
		52	## @end tex
		53	## @end iftex
		54	## @ifinfo
37	## @example	55	## @example
38	## a x a' - x + b b' = 0	56	## a x a' - x + b b' = 0
39	## @end example	57	## @end example
		58	## @end ifinfo
40	## @noindent	59	## @noindent
41	## or	60	## or
		61	## @iftex
		62	## @tex
		63	## $$ a^{ \rm T }x\,a - x + b^{ \rm T }b = 0, $$
		64	## @end tex
		65	## @end iftex
		66	## @ifinfo
42	## @example	67	## @example
43	## a' x a - x + b' b = 0,	68	## a' x a - x + b' b = 0,
44	## @end example	69	## @end example
		70	## @end ifinfo
45	## @noindent	71	## @noindent
46	## whichever is appropriate.	72	## whichever is appropriate.
47	## @end itemize	73	## @end itemize
Lines 54-60 Link Here
54	##	80	##
55	## Column-by-column solution method as suggested in	81	## Column-by-column solution method as suggested in
56	## Hammarling, @cite{Numerical Solution of the Stable, Non-Negative	82	## Hammarling, @cite{Numerical Solution of the Stable, Non-Negative
57	## Definite Lyapunov Equation}, IMA Journal of Numerical Analysis, Volume	83	## Definite Lyapunov Equation}, @acronym{IMA} Journal of Numerical Analysis, Volume
58	## 2, pages 303--323 (1982).	84	## 2, pages 303--323 (1982).
59	## @end deftypefn	85	## @end deftypefn
60		86




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{tvals}, @var{plist}] =} dre (@var{sys}, @var{q}, @var{r}, @var{qf}, @var{t0}, @var{tf}, @var{ptol}, @var{maxits})
## Solve the differential Riccati equation
## @ifinfo
## @example

## @end ifinfo
## @iftex
## @tex
## $$ -{dP \over dt} = A^{ \rm T } P+PA-PBR^{-1}B^{ \rm T } P+Q $$
## $$ P(t_f) = Q_f $$
## @end tex
## @end iftex
## for the @acronym{LTI} system sys.  Solution of 
## standard @acronym{LTI} state feedback optimization
## @ifinfo
## @example
##   min int(t0, tf) ( x' Q x + u' R u ) dt + x(tf)' Qf x(tf)
## @end example
## @end ifinfo
## @iftex
## @tex
## $$ \min \int_{t_0}^{t_f} x^{ \rm T } Q x + u^{ \rm T } R u dt + x(t_f)^{ \rm T } Q_f x(t_f) $$
## @end tex
## @end iftex
## optimal input is

## @end ifinfo
## @iftex
## @tex
## $$ u = - R^{-1} B^{ \rm T } P(t) x $$
## @end tex
## @end iftex
## @strong{Inputs}

## @item tvals
## time values at which @var{p}(@var{t}) is computed
## @item plist
## list values of @var{p}(@var{t}); @var{plist} @{ @var{i} @}
## is @var{p}(@var{tvals}(@var{i}))
## @end table
## @var{tvals} is selected so that:
## @iftex
## @tex
## $$ \Vert plist_{i} - plist_{i-1} \Vert < ptol $$
## @end tex
## @end iftex
## @ifinfo
## @example
## || Plist@{i@} - Plist@{i-1@} || < Ptol
## for ii=2:length(tvals)
## @end example
## @end ifinfo
## for every @var{i} between 2 and length(@var{tvals}).
## @end deftypefn

function [tvals, Plist] = dre (sys, Q, R, Qf, t0, tf, Ptol, maxits)

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} frdemo ()	20	## @deftypefn {Function File} {} frdemo ()
21	## Octave Controls toolbox demo: Frequency Response demo	21	## Octave Control Toolbox demo: Frequency Response demo.
22	## @end deftypefn	22	## @end deftypefn
23		23
24	## Author: David Clem	24	## Author: David Clem

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} freqchkw (@var{w})	20	## @deftypefn {Function File} {} freqchkw (@var{w})
21	## Used by @code{__freqresp__} to check that input frequency vector @var{w}	21	## Used by @command{__freqresp__} to check that input frequency vector @var{w}
22	## is valid.	22	## is valid.
23	## Returns boolean value.	23	## Returns boolean value.
24	## @end deftypefn	24	## @end deftypefn

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} __freqresp__ (@var{sys}, @var{USEW}, @var{w})	20	## @deftypefn {Function File} {} __freqresp__ (@var{sys}, @var{USEW}, @var{w})
21	## Frequency response function - used internally by @code{bode}, @code{nyquist}.	21	## Frequency response function - used internally by @command{bode}, @command{nyquist}.
22	## minimal argument checking; "do not attempt to do this at home"	22	## minimal argument checking; ``do not attempt to do this at home''.
23	##	23	##
24	## @strong{Inputs}	24	## @strong{Inputs}
25	## @table @var	25	## @table @var
Lines 33-39 Link Here
33	## @strong{Outputs}	33	## @strong{Outputs}
34	## @table @var	34	## @table @var
35	## @item @var{out}	35	## @item @var{out}
36	## vector of finite @math{G(jw)} entries (or @math{\|\|G(jw)\|\|} for MIMO)	36	## vector of finite @math{G(jw)} entries (or @math{\|\|G(jw)\|\|} for @acronym{MIMO})
37	## @item w	37	## @item w
38	## vector of corresponding frequencies	38	## vector of corresponding frequencies
39	## @end table	39	## @end table

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} gram (@var{a}, @var{b})	20	## @deftypefn {Function File} {} gram (@var{a}, @var{b})
21	## Return controllability grammian @var{m} of the continuous time system	21	## Return controllability gramian @var{m} of the continuous time system
22	## @math{dx/dt = a x + b u}.	22	## @math{dx/dt = a x + b u}.
23	##	23	##
24	## @var{m} satisfies @math{a m + m a' + b b' = 0}.	24	## @var{m} satisfies @math{a m + m a' + b b' = 0}.




## the number of data values.
##
## Both parameters @var{tstop} and @var{n} can be omitted and will be
## computed from the eigenvalues of the A Matrix.
## @end table
## @strong{Outputs}
## @table @var
## @item y
## Values of the impulse response.
## @item t
## Times of the impulse response.
## @end table
## @end deftypefn
## @seealso{step, __stepimp__}

## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
## Created: October 2, 1997




## intensities of independent Gaussian noise processes (as above)
## @item  q
## @itemx  r
## state, control weighting respectively.  Control @acronym{ARE} is
## @item  in_idx
## names or indices of controlled inputs (see @command{sysidx}, @command{cellidx})
##
## default: last dim(R) inputs are assumed to be controlled inputs, all
## others are assumed to be noise inputs.

## @strong{Outputs}
## @table @var
## @item    k
## system data structure format @acronym{LQG} optimal controller (Obtain A, B, C
## matrices with @command{sys2ss}, @command{sys2tf}, or @command{sys2zp} as
## appropriate).
## @item    p1
## Solution of control (state feedback) algebraic Riccati equation.
## @item    q1
## Solution of estimation algebraic Riccati equation.
## @item    ee
## Estimator poles.
## @item    es
## Controller poles.
## @end table
## @end deftypefn
## @seealso{h2syn, lqe, and lqr}




## @iftex
## @tex
## $$
##  J = \int_0^\infty x^{ \rm T } Q x + u^{ \rm T } R u
## $$
## @end tex
## @end iftex

## @iftex
## @tex
## $$
##  J = \int_0^\infty x^{ \rm T } Q x + u^{ \rm T } R u + 2 x^{ \rm T } Z u
## $$
## @end tex
## @end iftex

## @end table
##
## @strong{Reference}
## Anderson and Moore, @cite{Optimal control: linear quadratic methods},
## Prentice-Hall, 1990, pp. 56--58.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{y}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
## Produce output for a linear simulation of a system; produces 
## a plot for the output of the system, @var{sys}.
##
## @var{u} is an array that contains the system's inputs.  Each row in @var{u}
## corresponds to a different time step.  Each column in @var{u} corresponds to a
## different input.  @var{t} is an array that contains the time index of the
## system; @var{t} should be regularly spaced.  If initial conditions are required
## on the system, the @var{x0} vector should be added to the argument list.
##
## When the lsim function is invoked a plot is not displayed; 
## however, the data is returned in @var{y} (system output)
## and @var{x} (system states).
## system.  T should be regularly spaced.  If initial conditions are required
## on the system, the x0 vector should be added to the argument list.
##
## When the lsim function is invoked with output parameters:
## [y,x] = lsim(sys,u,t,[x0])
## a plot is not displayed, however, the data is returned in y = system output
## and x = system states.
## @end deftypefn

## Author: David Clem




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{out} =} ltifr (@var{a}, @var{b}, @var{w})
## @deftypefnx {Function File} {@var{out} =} ltifr (@var{sys}, @var{w})
## Linear time invariant frequency response of single-input systems.
##
## @strong{Inputs}
## @table @var
## @item a

## @item w
## vector of frequencies
## @end table
## @strong{Output}
## @table @var
## @item out
## frequency response, that is:
## @end table
## @iftex
## @tex
## $$ G(j\omega) = (j\omega\,I-A)^{-1}B $$
## @end tex
## @end iftex
## @ifinfo
## @example
##                            -1
##              G(s) = (jw I-A) B
## @end example
## @end ifinfo
## for complex frequencies @math{s = jw}.
## @end deftypefn





## @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c})
## @deftypefnx {Function File} {} lyap (@var{a}, @var{b})
## Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart
## algorithm (Communications of the @acronym{ACM}, 1972).
##
## If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns
## the solution of the  Sylvester equation

##     a x + x b + c = 0
## @end example
## @end ifinfo
## If only @code{(a, b)} are specified, then @command{lyap} returns the
## solution of the Lyapunov equation
## @iftex
## @tex
##   $$ A^{ \rm T } X + X A + B = 0 $$
## @end tex
## @end iftex
## @ifinfo

## If @var{b} is not square, then @code{lyap} returns the solution of either
## @iftex
## @tex
##   $$ A^{ \rm T } X + X A + B^{ \rm T } B = 0 $$
## @end tex
## @end iftex
## @ifinfo

## or
## @iftex
## @tex
##   $$ A X + X A^{ \rm T } + B B^{ \rm T } = 0 $$
## @end tex
## @end iftex
## @ifinfo




## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs})
## Produce Nichols plot of a system.
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure (must be either purely continuous or discrete; 
## see @command{is_digital}).
## @item w
## Frequency values for evaluation.
## @itemize
## @item if sys is continuous, then nichols evaluates @math{G(jw)}.
## @item if sys is discrete, then nichols evaluates @math{G(exp(jwT))}, 
## where @var{T}=@var{sys}. @var{tsam} is the system sampling time.
## @item the default frequency range is selected as follows (These
##        steps are @strong{not} performed if @var{w} is specified):
## @enumerate
## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
## @var{w}=0 (@math{jw=0} or @math{exp(jwT)=1}) and select the frequency range 
## based on the breakpoint locations of the frequencies.
## @item if sys is discrete time, the frequency range is limited to jwT in 
## @iftex
## @tex
## $ [0,~2p\,\pi] $.
## @end tex
## @end iftex
## @ifinfo
## [0,2p*pi].
## @end ifinfo
## @item A ``smoothing'' routine is used to ensure that the plot phase does
## not change excessively from point to point and that singular points 
## (e.g., crossovers from +/- 180) are accurately shown.
## @end enumerate
## @end itemize
## @item outputs
## @itemx inputs
## the names or indices of the output(s) and input(s) to be used in the 
## frequency response; see @command{sysprune}.
## @end table
## @strong{Outputs}
## @table @var
## @item mag
## @itemx phase
## The magnitude and phase of the frequency response @math{G(jw)} or 
## @math{G(exp(jwT))} at the selected frequency values.
## @item w
## The vector of frequency values used.
## @end table
## If no output arguments are given, @command{nichols} plots the results to the screen.
## Descriptive labels are automatically placed. See @command{xlabel}, 
## @command{ylabel}, @command{title}, and @command{replot}.
##
## Note: if the requested plot is for an @acronym{MIMO} system, @var{mag} is set to
## @iftex
## @tex
## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
## @end tex
## @end iftex
## @ifinfo
## ||G(jw)|| or ||G(exp(jwT))||
## @end ifinfo
## and phase information is not computed.
## @end deftypefn

function [mag, phase, w] = nichols (sys, w, outputs, inputs)




## plot is printed to the screen.
##
## Compute the frequency response of a system.
##
## @strong{Inputs} (pass as empty to get default values)
## @table @var
## @item sys
## system data structure (must be either purely continuous or discrete;
## see @code{is_digital})
## @item w
## frequency values for evaluation.
## If sys is continuous, then bode evaluates @math{G(@var{jw})}; 
## if sys is discrete, then bode evaluates @math{G(exp(@var{jwT}))},
## where @var{T} is the system sampling time.
## @item default
## the default frequency range is selected as follows: (These
## steps are @strong{not} performed if @var{w} is specified)
## @end table
## @enumerate
## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
## @var{w}=0 (@var{jw}=0 or @math{exp(@var{jwT})=1}) and select the frequency
## range based on the breakpoint locations of the frequencies.
## @item if @var{sys} is discrete time, the frequency range is limited

## [0,2p*pi]
## @end ifinfo
## @iftex
## @tex
## $ [ 0,2 \, p \pi ] $
## @end tex
## @end iftex
## @item A ``smoothing'' routine is used to ensure that the plot phase does
## not change excessively from point to point and that singular
## points (e.g., crossovers from +/- 180) are accurately shown.
## @end enumerate
## outputs, inputs: names or indices of the output(s) and input(s) to be 
## used in the frequency response; see sysprune.
##
## @strong{Inputs} (pass as empty to get default values)
## @table @var
## @item   atol
## for interactive nyquist plots: atol is a change-in-slope tolerance
## for the of asymptotes (default = 0; 1e-2 is a good choice).  This allows

## @itemx   imagp
## the real and imaginary parts of the frequency response
## @math{G(jw)} or @math{G(exp(jwT))} at the selected frequency values.
## @item w
## the vector of frequency values used
## @end table
##

## interactively if they wish to zoom in (remove asymptotes)
## Descriptive labels are automatically placed.
##
## Note: if the requested plot is for an @acronym{MIMO} system, a warning message is
## presented; the returned information is of the magnitude
## @iftex
## @tex
## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
## @end tex
## @end iftex
## @ifinfo
## ||G(jw)|| or ||G(exp(jwT))||
## @end ifinfo
## only; phase information is not computed.
## @end deftypefn

## Author: R. Bruce Tenison <btenison@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} obsv (@var{sys}, @var{c})
## @deftypefnx {Function File} {} obsv (@var{a}, @var{c})
## Build observability matrix:
## @iftex
## @tex
## $$ Q_b = \left[ \matrix{  C       \cr
##                           C\,A    \cr
##                           C\,A^2  \cr
##                           \vdots  \cr
##                           C\,A^{n-1} } \right ] $$
## @end tex
## @end iftex
## @ifinfo
## @example
## @group
##      | C        |

##      | CA^(n-1) |
## @end group
## @end example
## @end ifinfo
## of a system data structure or the pair (@var{a}, @var{c}).
##
## The numerical properties of @command{is_observable}
##
## The numerical properties of is_observable()
## are much better for observability tests.
## @end deftypefn


Lines 17-26 Link Here

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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} place (@var{sys}, @var{p})	20	## @deftypefn {Function File} {@var{K} =} place (@var{sys}, @var{p})
21	## Computes the matrix K such that if the state	21	## Computes the matrix @var{K} such that if the state
22	## is feedback with gain K, then the eigenvalues of the closed loop	22	## is feedback with gain @var{K}, then the eigenvalues of the closed loop
23	## system (i.e. A-BK) are those specified in the vector @var{p}.	23	## system (i.e. @math{A-BK}) are those specified in the vector @var{p}.
24	##	24	##
25	## Version: Beta (May-1997): If you have any comments, please let me know.	25	## Version: Beta (May-1997): If you have any comments, please let me know.
26	## (see the file place.m for my address)	26	## (see the file place.m for my address)

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(-)octave-2.1.58/scripts/control/base/pzmap.m (-5 / +13 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{zer}, @var{pol}]=} pzmap (@var{sys})	20	## @deftypefn {Function File} {[@var{zer}, @var{pol}] =} pzmap (@var{sys})
21	## Plots the zeros and poles of a system in the complex plane.	21	## Plots the zeros and poles of a system in the complex plane.
22	## @strong{Inputs}	22	##
23	## @var{sys} system data structure	23	## @strong{Input}
		24	## @table @var
		25	## @item sys
		26	## System data structure.
		27	## @end table
24	##	28	##
25	## @strong{Outputs}	29	## @strong{Outputs}
		30	## @table @var
		31	## @item pol
		32	## @item zer
26	## if omitted, the poles and zeros are plotted on the screen.	33	## if omitted, the poles and zeros are plotted on the screen.
27	## otherwise, pol, zer are returned as the system poles and zeros.	34	## otherwise, @var{pol} and @var{zer} are returned as the
28	## (see sys2zp for a preferable function call)	35	## system poles and zeros (see @command{sys2zp} for a preferable function call).
		36	## @end table
29	## @end deftypefn	37	## @end deftypefn
30		38
31	function [zer, pol]=pzmap (sys)	39	function [zer, pol]=pzmap (sys)

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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	##@deftypefn {Function File} {} rldemo (@var{inputs})	20	## @deftypefn {Function File} {} rldemo (@var{inputs})
21	##Octave Controls toolbox demo: Root Locus demo	21	## Octave Control toolbox demo: Root Locus demo.
22	##@end deftypefn	22	## @end deftypefn
23		23
24	## Author: David Clem	24	## Author: David Clem
25	## Created: August 15, 1994	25	## Created: August 15, 1994




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{rldata}, @var{k}] =} rlocus (@var{sys}[, @var{increment}, @var{min_k}, @var{max_k}])
## @format
## [rldata, k] = rlocus(sys[,increment,min_k,max_k])
## Displays root locus plot of the specified SISO system.
##
## Displays root locus plot of the specified @acronym{SISO} system.
## @example
## @group
##        -----   ---     --------
##    --->| + |---|k|---->| SISO |----------->
##        -----   ---     --------        |
##        - ^                             |
##          |_____________________________|
## @end group
## @end example
##
## @strong{Inputs}
## @table @var
## @item sys
## system data structure
## @item min_k
## Minimum value of @var{k}
## @item max_k
## Maximum value of @var{k}
## @item increment
## The increment used in computing gain values
## @end table
##
## @strong{Outputs}
##
## Plots the root locus to the screen.
## @table @var 
## @item rldata
## Data points plotted: in column 1 real values, in column 2 the imaginary values.
## @item k
## Gains for real axis break points.
## @end table
## @end deftypefn

## Author: David Clem




## @deftypefn {Function File} {[@var{y}, @var{t}] =} __stepimp__ (@var{sitype}, @var{sys} [, @var{inp}, @var{tstop}, @var{n}])
## Impulse or step response for a linear system.
## The system can be discrete or multivariable (or both).
## This m-file contains the ``common code'' of step and impulse.
##
## Produces a plot or the response data for system @var{sys}.
##
## Limited argument checking; ``do not attempt to do this at home''.
## Used internally in @command{impulse}, @command{step}. Use @command{step}
## or @command{impulse} instead.
## @end deftypefn
## @seealso{step, impulse}

## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
## Created: October 2, 1997




## the number of data values.
##
## Both parameters @var{tstop} and @var{n} can be omitted and will be
## computed from the eigenvalues of the A Matrix.
## @end table
## @strong{Outputs}
## @table @var
## @item y
## Values of the step response.
## @item t
## Times of the step response.
## @end table
##
## When invoked with the output parameter @var{y} the plot is not displayed.
## @end deftypefn
## @seealso{impulse and __stepimp__}





## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{zr} =} tzero2 (@var{a}, @var{b}, @var{c}, @var{d}, @var{bal})
## Compute the transmission zeros of @var{a}, @var{b}, @var{c}, @var{d}.
##
## @var{bal} = balancing option (see balance); default is @code{"B"}.
##
## Needs to incorporate @command{mvzero} algorithm to isolate finite zeros; 
## use @command{tzero} instead.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{zer}, @var{gain}] =} tzero (@var{a}, @var{b}, @var{c}, @var{d}, @var{opt})
## @deftypefnx {Function File} {[@var{zer}, @var{gain}] =} tzero (@var{sys}, @var{opt})
## Compute transmission zeros of a continuous system:
## @iftex
## @tex
## $$ \dot x = A\,x + B\,u $$
## $$ y = C\,x + D\,u $$
## @end tex
## @end iftex
## @ifinfo
## @example
## .
## x = Ax + Bu
## y = Cx + Du
## @end example
## @end ifinfo
## or of a discrete one:
## @iftex
## @tex
## $$ x_{k+1} = A\,x_k + B\,u_k $$
## $$ y_k = C\,x_k + D\,u_k $$
## @end tex
## @end iftex
## @ifinfo
## @example
## x(k+1) = A x(k) + B u(k)
## y(k)   = C x(k) + D u(k)
## @end example
## @end ifinfo
## 
## @strong{Outputs}
## @table @var
## @item zer
##  transmission zeros of the system
## @item gain
## leading coefficient (pole-zero form) of @acronym{SISO} transfer function
## returns gain=0 if system is multivariable
## @end table
## @strong{References}
## @enumerate
## @item Emami-Naeini and Van Dooren, Automatica, 1982.
## @item Hodel, @cite{Computation of Zeros with Balancing}, 1992 Lin. Alg. Appl.
## @end enumerate
## @end deftypefn






## -*- texinfo -*-
## @deftypefn {Function File} {} dgkfdemo ()
## Octave Controls toolbox demo: 
## @iftex
## @tex
## $ { \cal H }_2 $/$ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-2/H-infinity
## @end ifinfo
## options demos.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 18-45 Link Here

(-)octave-2.1.58/scripts/control/hinf/dhinfdemo.m (-6 / +34 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} dhinfdemo ()	20	## @deftypefn {Function File} {} dhinfdemo ()
21	## Demonstrate the functions available for designining a discrete	21	## Demonstrate the functions available to design a discrete
22	## H_infinity controller. This is not a true discrete design. The	22	## @iftex
		23	## @tex
		24	## $ { \cal H }_\infty $
		25	## @end tex
		26	## @end iftex
		27	## @ifinfo
		28	## H-infinity
		29	## @end ifinfo
		30	## controller. This is not a true discrete design. The
23	## design is carried out in continuous time while the effect of sampling	31	## design is carried out in continuous time while the effect of sampling
24	## is described by a bilinear transformation of the sampled system.	32	## is described by a bilinear transformation of the sampled system.
25	## This method works quite well if the sampling period is "small"	33	## This method works quite well if the sampling period is "small"
26	## compared to the plant time constants.	34	## compared to the plant time constants.
27	##	35	##
28	## Continuous plant:	36	## Continuous plant:
29	##	37	## @iftex
		38	## @tex
		39	## $$ G(s) = { 1 \over (s+2) (s+1) } $$
		40	## @end tex
		41	## @end iftex
		42	## @ifinfo
30	## @example	43	## @example
		44	## @group
31	## 1	45	## 1
32	## G(s) = --------------	46	## G(s) = --------------
33	## (s + 2)(s + 1)	47	## (s + 2)(s + 1)
		48	## @end group
34	## @end example	49	## @end example
		50	## @end ifinfo
35	##	51	##
36	## Discretised plant with ZOH (Sampling period = Ts = 1 second):	52	## Discretised plant with @acronym{ZOH} (Sampling period = @var{Ts} = 1 second):
37	##	53	## @iftex
		54	## @tex
		55	## $$ G(z) = { 0.39958\,z + 0.14700 \over (z - 0.36788) (z - 0.13533) } $$
		56	## @end tex
		57	## @end iftex
		58	## @ifinfo
38	## @example	59	## @example
		60	## @group
39	## 0.39958z + 0.14700	61	## 0.39958z + 0.14700
40	## G(s) = --------------------------	62	## G(z) = --------------------------
41	## (z - 0.36788)(z - 0.13533)	63	## (z - 0.36788)(z - 0.13533)
		64	## @end group
		65	## @end example
		66	## @end ifinfo
42	##	67	##
		68	## @example
		69	## @group
43	## +----+	70	## +----+
44	## -------------------->\| W1 \|---> v1	71	## -------------------->\| W1 \|---> v1
45	## z \| +----+	72	## z \| +----+
Lines 52-57 Link Here
52	## \| +---+ \|	79	## \| +---+ \|
53	## -----\| K \|<-------	80	## -----\| K \|<-------
54	## +---+	81	## +---+
		82	## @end group
55	## @end example	83	## @end example
56	##	84	##
57	## @noindent	85	## @noindent




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} h2norm (@var{sys})
## Computes the 
## @iftex
## @tex
## $ { \cal H }_2 $
## @end tex
## @end iftex
## @ifinfo
## H-2
## @end ifinfo
## norm of a system data structure (continuous time only).
##
## Reference:
## Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions to Standard} 
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

      M = lyap (a,b*b');
    endif
    if( min(real(eig(M))) < 0)
      error("h2norm: gramian not >= 0 (lightly damped modes?)")
    endif

    h2gain = sqrt(trace(d'*d + c*M*c'));




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{K}, @var{gain}, @var{kc}, @var{kf}, @var{pc}, @var{pf}] = } h2syn (@var{asys}, @var{nu}, @var{ny}, @var{tol})
## Design 
## @iftex
## @tex
## $ { \cal H }_2 $
## @end tex
## @end iftex
## @ifinfo
## H-2
## @end ifinfo
## optimal controller per procedure in 
## Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions to Standard}
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
##
## Discrete-time control per Zhou, Doyle, and Glover, @cite{Robust and optimal control}, Prentice-Hall, 1996.
## CONTROL, Prentice-Hall, 1996
##
## @strong{Inputs}
## @table @var
## @item asys
## system data structure (see ss, sys2ss)
## @itemize @bullet
## @item controller is implemented for continuous time systems
## @item controller is @strong{not} implemented for discrete time systems
## @end itemize
## @item nu
## number of controlled inputs
## @item ny
## number of measured outputs
## @item tol
## threshold for 0.  Default: 200*@code{eps}
## @end table
##
## @strong{Outputs}

## @item    kf
## state estimator (packed)
## @item    pc
## @acronym{ARE} solution matrix for regulator subproblem
## @item    pf
## @acronym{ARE} solution matrix for filter subproblem
## @end table
## @end deftypefn


Lines 17-24 Link Here

(-)octave-2.1.58/scripts/control/hinf/hinf_ctr.m (-2 / +14 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} hinf_ctr (@var{dgs}, @var{f}, @var{h}, @var{z}, @var{g})	20	## @deftypefn {Function File} {@var{K} =} hinf_ctr (@var{dgs}, @var{f}, @var{h}, @var{z}, @var{g})
21	## Called by @code{hinfsyn} to compute the H_inf optimal controller.	21	## Called by @code{hinfsyn} to compute the
		22	## @iftex
		23	## @tex
		24	## $ { \cal H }_\infty $
		25	## @end tex
		26	## @end iftex
		27	## @ifinfo
		28	## H-infinity
		29	## @end ifinfo
		30	## optimal controller.
22	##	31	##
23	## @strong{Inputs}	32	## @strong{Inputs}
24	## @table @var	33	## @table @var
Lines 31-37 Link Here
31	## final gamma value	40	## final gamma value
32	## @end table	41	## @end table
33	## @strong{Outputs}	42	## @strong{Outputs}
		43	## @table @var
		44	## @item K
34	## controller (system data structure)	45	## controller (system data structure)
		46	## @end table
35	##	47	##
36	## Do not attempt to use this at home; no argument checking performed.	48	## Do not attempt to use this at home; no argument checking performed.
37	## @end deftypefn	49	## @end deftypefn




## -*- texinfo -*-
## @deftypefn {Function File} {} hinfdemo ()
##
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## design demos for continuous @acronym{SISO} and @acronym{MIMO} systems and a
## discrete system.  The @acronym{SISO} system is difficult to control because
## it is non-minimum-phase and unstable. The second design example
## controls the @command{jet707} plant, the linearized state space model of a
## Boeing 707-321 aircraft at @var{v}=80 m/s 
## @iftex
## @tex
## ($M = 0.26$, $G_{a0} = -3^{\circ}$, ${\alpha}_0 = 4^{\circ}$, ${\kappa}= 50^{\circ}$).
## @end tex
## @end iftex
## @ifinfo
## (@var{M} = 0.26, @var{Ga0} = -3 deg, @var{alpha0} = 4 deg, @var{kappa} = 50 deg).
## @end ifinfo
## Inputs: (1) thrust and (2) elevator angle
## Outputs: (1) airspeed and (2) pitch angle. The discrete system is a
## stable and second order.
##
## @table @asis
## @item @acronym{SISO} plant:
##
## @iftex
## @tex
## $$ G(s) = { s-2 \over (s+2) (s-1) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
## @group
##                 s - 2
##      G(s) = --------------
##             (s + 2)(s - 1)
## @end group
## @end example
## @end ifinfo
##
## @example
## @group
##
##                               +----+
##          -------------------->| W1 |---> v1
##      z   |                    +----+
##      ----|-------------+
##          |             |
##          |    +---+    v   y  +----+
##        u *--->| G |--->O--*-->| W2 |---> v2
##          |    +---+       |   +----+

##          -----| K |<-------
##               +---+
## @end group
## @end example
## 
## @iftex
## @tex
## $$ { \rm min } \Vert T_{vz} \Vert _\infty $$
## @end tex
## @end iftex
## @ifinfo
## @example
## min || T   ||
##         vz   infty
## @end example
## @end ifinfo
##
## @var{W1} und @var{W2} are the robustness and performance weighting
## functions.
##
## @item @acronym{MIMO} plant:
## The optimal controller minimizes the 
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## norm of the
## augmented plant @var{P} (mixed-sensitivity problem):
## @example
## @group
##      w
##       1 -----------+

##             |          +----+      |   +----+
##             |                      |
##             ^                      v
##             u                       y (to K)
##          (from controller K)
## @end group
## @end example
##
## @iftex
## @tex
## $$ \left [ \matrix{ z_1 \cr
##                     z_2 \cr
##                     y   } \right ] =  
##  P \left [ \matrix{ w_1 \cr
##                     w_2 \cr
##                     u   } \right ] $$
## @end tex
## @end iftex
## @ifinfo
## @example
## @group
##                   +    +           +    +
##                   | z  |           | w  |
##                   |  1 |           |  1 |

##                   | y  |           | u  |
##                   +    +           +    +
## @end group
## @end example
## @end ifinfo
##
## @item Discrete system:
## This is not a true discrete design. The design is carried out
## in continuous time while the effect of sampling is described by
## a bilinear transformation of the sampled system.
## This method works quite well if the sampling period is ``small''
## compared to the plant time constants.
##
## @item The continuous plant:
## @iftex
## @tex
## $$ G(s) = { 1 \over (s+2)(s+1) } $$
## @end tex
## @end iftex
##
## @ifinfo
## @example
## @group
##                    1
##      G (s) = --------------
##       k      (s + 2)(s + 1)
##
## @end group
## @end example
## @end ifinfo
##
## is discretised with a @acronym{ZOH} (Sampling period = @var{Ts} = 1 second):
## @iftex
## @tex
## $$ G(z) = { 0.199788\,z + 0.073498 \over (z - 0.36788) (z - 0.13534) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
## @group
##
##                0.199788z + 0.073498
##      G(z) = --------------------------
##             (z - 0.36788)(z - 0.13534)
## @end group
## @end example
## @end ifinfo
##
## @example
## @group
##
##                               +----+
##          -------------------->| W1 |---> v1
##      z   |                    +----+
##      ----|-------------+
##          |             |
##          |    +---+    v      +----+
##          *--->| G |--->O--*-->| W2 |---> v2
##          |    +---+       |   +----+

##          -----| K |<-------
##               +---+
## @end group
## @end example
## @iftex
## @tex
## $$ { \rm min } \Vert T_{vz} \Vert _\infty $$
## @end tex
## @end iftex
## @ifinfo
## @example
## min || T   ||
##         vz   infty
## @end example
## @end ifinfo
## @var{W1} and @var{W2} are the robustness and performance weighting
## functions.
## @end table
## @end deftypefn






## -*- texinfo -*-
## @deftypefn {Function File} {[@var{g}, @var{gmin}, @var{gmax}] =} hinfnorm (@var{sys}, @var{tol}, @var{gmin}, @var{gmax}, @var{ptol})
## Computes the 
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## norm of a system data structure.
##
## @strong{Inputs}
## @table @var
## @item sys
## system data structure
## @item tol
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## norm search tolerance (default: 0.001)
## @item gmin
## minimum value for norm search (default: 1e-9)
## @item gmax

## pole tolerance:
## @itemize @bullet
## @item if sys is continuous, poles with
## @iftex
## @tex
## $ \vert {\rm real}(pole) \vert < ptol \Vert H \Vert $
## @end tex
## @end iftex
## @ifinfo
## @math{ |real(pole))| < ptol*||H|| }
## @end ifinfo
## (@var{H} is appropriate Hamiltonian)
## are considered to be on the imaginary axis.
##
## @item if sys is discrete, poles with
## @iftex
## @tex
## $ \vert { \rm pole } - 1 \vert < ptol \Vert [ s_1 ~ s_2 ] \Vert $
## @end tex
## @end iftex
## @ifinfo
## @math{|abs(pole)-1| < ptol*||[s1,s2]||}
## @end ifinfo
## (appropriate symplectic pencil)
## are considered to be on the unit circle.
##
## @item Default value: 1e-9
## @end itemize
## @end table
##

## if the system is unstable.
## @item gmin
## @itemx gmax
## Actual system gain lies in the interval [@var{gmin}, @var{gmax}].
## @end table
##
## References:
## Doyle, Glover, Khargonekar, Francis, @cite{State-space solutions to standard}
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{control problems}, @acronym{IEEE} @acronym{TAC} August 1989;
## Iglesias and Glover, @cite{State-Space approach to discrete-time}
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-infinity}
## @end ifinfo
## @cite{control}, Int. J. Control, vol 54, no. 5, 1991;
## Zhou, Doyle, Glover, @cite{Robust and Optimal Control}, Prentice-Hall, 1996.
## @end deftypefn

function [g, gmin, gmax] = hinfnorm (sys, tol, gmin, gmax, ptol)

Lines 20-32 Link Here

(-)octave-2.1.58/scripts/control/hinf/hinfsyn_chk.m (-6 / +34 lines)
20	## @deftypefn {Function File} {[@var{retval}, @var{pc}, @var{pf}] =} hinfsyn_chk (@var{a}, @var{b1}, @var{b2}, @var{c1}, @var{c2}, @var{d12}, @var{d21}, @var{g}, @var{ptol})	20	## @deftypefn {Function File} {[@var{retval}, @var{pc}, @var{pf}] =} hinfsyn_chk (@var{a}, @var{b1}, @var{b2}, @var{c1}, @var{c2}, @var{d12}, @var{d21}, @var{g}, @var{ptol})
21	## Called by @code{hinfsyn} to see if gain @var{g} satisfies conditions in	21	## Called by @code{hinfsyn} to see if gain @var{g} satisfies conditions in
22	## Theorem 3 of	22	## Theorem 3 of
23	## Doyle, Glover, Khargonekar, Francis, "State Space Solutions to Standard	23	## Doyle, Glover, Khargonekar, Francis, @cite{State Space Solutions to Standard}
24	## H2 and Hinf Control Problems", IEEE TAC August 1989	24	## @iftex
		25	## @tex
		26	## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
		27	## @end tex
		28	## @end iftex
		29	## @ifinfo
		30	## @cite{H-2 and H-infinity}
		31	## @end ifinfo
		32	## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
25	##	33	##
26	## @strong{Warning} Do not attempt to use this at home; no argument	34	## @strong{Warning:} do not attempt to use this at home; no argument
27	## checking performed.	35	## checking performed.
28	##	36	##
29	## @strong{Inputs} as returned by @code{is_dgkf}, except for:	37	## @strong{Inputs}
		38	##
		39	## As returned by @code{is_dgkf}, except for:
30	## @table @var	40	## @table @var
31	## @item g	41	## @item g
32	## candidate gain level	42	## candidate gain level
Lines 39-47 Link Here
39	## @item retval	49	## @item retval
40	## 1 if g exceeds optimal Hinf closed loop gain, else 0	50	## 1 if g exceeds optimal Hinf closed loop gain, else 0
41	## @item pc	51	## @item pc
42	## solution of "regulator" H-inf ARE	52	## solution of ``regulator''
		53	## @iftex
		54	## @tex
		55	## $ { \cal H }_\infty $
		56	## @end tex
		57	## @end iftex
		58	## @ifinfo
		59	## H-infinity
		60	## @end ifinfo
		61	## @acronym{ARE}
43	## @item pf	62	## @item pf
44	## solution of "filter" H-inf ARE	63	## solution of ``filter''
		64	## @iftex
		65	## @tex
		66	## $ { \cal H }_\infty $
		67	## @end tex
		68	## @end iftex
		69	## @ifinfo
		70	## H-infinity
		71	## @end ifinfo
		72	## @acronym{ARE}
45	## @end table	73	## @end table
46	## Do not attempt to use this at home; no argument checking performed.	74	## Do not attempt to use this at home; no argument checking performed.
47	## @end deftypefn	75	## @end deftypefn




## @strong{Inputs} input system is passed as either
## @table @var
## @item asys
## system data structure (see @command{ss}, @command{sys2ss})
## @itemize @bullet
## @item controller is implemented for continuous time systems
## @item controller is @strong{not} implemented for discrete time systems  (see
## bilinear transforms in @command{c2d}, @command{d2c})
## @end itemize
## @item nu
## number of controlled inputs
## @item ny
## number of measured outputs
## @item gmin
## initial lower bound on 
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## optimal gain
## @item gmax
## initial upper bound on 
## @iftex
## @tex
## $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-infinity
## @end ifinfo
## Optimal gain.
## @item gtol
## Gain threshold.  Routine quits when @var{gmax}/@var{gmin} < 1+tol.
## @item ptol
## poles with @code{abs(real(pole))} 
## @iftex
## @tex
## $ < ptol \Vert H \Vert $
## @end tex
## @end iftex
## @ifinfo
## < ptol*||H|| 
## @end ifinfo
## (@var{H} is appropriate
## Hamiltonian) are considered to be on the imaginary axis.
## Default: 1e-9.
## @item tol
## threshold for 0.  Default: 200*@code{eps}.
##
## @var{gmax}, @var{min}, @var{tol}, and @var{tol} must all be postive scalars.
## @end table
## @strong{Outputs}
## @table @var
## @item k
## System controller.
## @item g
## Designed gain value.
## @item gw
## Closed loop system.
## @item xinf
## @acronym{ARE} solution matrix for regulator subproblem.
## @item yinf
## @acronym{ARE} solution matrix for filter subproblem.
## @end table
##
## References:
## @enumerate
## @item Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions
## to Standard}
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
##
## @item Maciejowksi, J.M., @cite{Multivariable feedback design},
## Addison-Wesley, 1989, @acronym{ISBN} 0-201-18243-2.
##
## @item Keith Glover and John C. Doyle, @cite{State-space formulae for all
## stabilizing controllers that satisfy an}
## @iftex
## @tex
## $ { \cal H }_\infty $@cite{norm}
## @end tex
## @end iftex
## @ifinfo
## @cite{H-infinity-norm}
## @end ifinfo
## @cite{bound and relations to risk sensitivity},
## Systems & Control Letters 11, Oct. 1988, pp 167--172.
## @end enumerate
## @end deftypefn


Lines 20-27 Link Here

(-)octave-2.1.58/scripts/control/hinf/hinfsyn_ric.m (-2 / +2 lines)
20	## @deftypefn {Function File} {[@var{xinf}, @var{x_ha_err}] =} hinfsyn_ric (@var{a}, @var{bb}, @var{c1}, @var{d1dot}, @var{r}, @var{ptol})	20	## @deftypefn {Function File} {[@var{xinf}, @var{x_ha_err}] =} hinfsyn_ric (@var{a}, @var{bb}, @var{c1}, @var{d1dot}, @var{r}, @var{ptol})
21	## Forms	21	## Forms
22	## @example	22	## @example
23	## xx = ([BB; -C1'd1dot]/R) [d1dot'*C1 BB'];	23	## xx = ([bb; -c1'd1dot]/r) [d1dot'*c1 bb'];
24	## Ha = [A 0A; -C1'C1 -A'] - xx;	24	## Ha = [a 0a; -c1'c1 - a'] - xx;
25	## @end example	25	## @end example
26	## and solves associated Riccati equation.	26	## and solves associated Riccati equation.
27	## The error code @var{x_ha_err} indicates one of the following	27	## The error code @var{x_ha_err} indicates one of the following




## -*- texinfo -*-
## @deftypefn {Function File} {[@var{retval}, @var{dgkf_struct} ] =} is_dgkf (@var{asys}, @var{nu}, @var{ny}, @var{tol} )
## Determine whether a continuous time state space system meets
## assumptions of @acronym{DGKF} algorithm.
## Partitions system into:
## @example
## [dx/dt]   [A  | Bw  Bu  ][w]
## [ z   ] = [Cz | Dzw Dzu ][u]
## [ y   ]   [Cy | Dyw Dyu ]
## @end example
## or similar discrete-time system.
## If necessary, orthogonal transformations @var{qw}, @var{qz} and nonsingular
## transformations @var{ru}, @var{ry} are applied to respective vectors
## @var{w}, @var{z}, @var{u}, @var{y} in order to satisfy @acronym{DGKF} assumptions.
## Loop shifting is used if @var{dyu} block is nonzero.
##
## @strong{Inputs}

## @item        ny
## number of measured outputs
## @item        tol
## threshold for 0; default: 200*@code{eps}.
## @end table
## @strong{Outputs}
## @table @var
## @item    retval
## true(1) if system passes check, false(0) otherwise
## @item    dgkf_struct
## data structure of @command{is_dgkf} results.  Entries:
## @table @var
## @item      nw
## @itemx     nz

## @end table
## @end table
## @code{is_dgkf} exits with an error if the system is mixed
## discrete/continuous.
##
## @strong{References}
## @table @strong
## @item [1]
## Doyle, Glover, Khargonekar, Francis, @cite{State Space Solutions to Standard}
## @iftex
## @tex
## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## @cite{H-2 and H-infinity}
## @end ifinfo
## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
## @item [2]
## Maciejowksi, J.M., @cite{Multivariable Feedback Design}, Addison-Wesley, 1989.
## @end table
## @end deftypefn





## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{W} =} wgt1o (@var{vl}, @var{vh}, @var{fc})
## State space description of a first order weighting function.
##
## Weighting function are needed by the 
## @iftex
## @tex
## $ { \cal H }_2 / { \cal H }_\infty $
## @end tex
## @end iftex
## @ifinfo
## H-2/H-infinity
## @end ifinfo
## design procedure.
## These function are part of the augmented plant @var{P}
## (see @command{hinfdemo} for an application example).
##
## @strong{Inputs}
## @table @var
## @item vl
## Gain at low frequencies.
## @item vh
## Gain at high frequencies.
## @item fc
## Corner frequency (in Hz, @strong{not} in rad/sec)
## @end table
##
## @strong{Output}
## @table @var
## @item W
## Weighting function, given in form of a system data structure.
## @end table
## @end deftypefn

## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>

Lines 16-33 Link Here

(-)octave-2.1.58/scripts/control/obsolete/minfo.m (-11 / +18 lines)
16	## along with Octave; see the file COPYING. If not, write to the Free	16	## along with Octave; see the file COPYING. If not, write to the Free
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## function [systype, nout, nin, ncstates, ndstates] = minfo(inmat)	19	## -- texinfo --
		20	## @deftypefn {Function File} {[@var{systype}, @var{nout}, @var{nin}, @var{ncstates}, @var{ndstates}] =} minfo (@var{inmat})
		21	## Determines the type of system matrix. @var{inmat} can be a varying,
		22	## a system, a constant, and an empty matrix.
20	##	23	##
21	## MINFO: Determines the type of system matrix. INMAT can be	24	## @strong{Outputs}
22	## a varying(*), system, constant, and empty matrix.	25	## @table @var
23	##	26	## @item systype
24	## Returns:	27	## Can be one of: varying, system, constant, and empty.
25	## systype can be one of:	28	## @item nout
26	## varying, system, constant, and empty	29	## The number of outputs of the system.
27	## nout is the number of outputs of the system	30	## @item nin
28	## nin is the number of inputs of the system	31	## The number of inputs of the system.
29	## ncstates is the number of continuous states of the system	32	## @item ncstates
30	## ndstates is the number of discrete states of the system	33	## The number of continuous states of the system.
		34	## @item ndstates
		35	## The number of discrete states of the system.
		36	## @end table
		37	## @end deftypefn
31		38
32	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>	39	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>
33	## Created: July 29, 1994	40	## Created: July 29, 1994

Lines 18-24 Link Here

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} syschnames (@var{sys}, @var{opt}, @var{list}, @var{names})	20	## @deftypefn {Function File} {} syschnames (@var{sys}, @var{opt}, @var{list}, @var{names})
21	## Superseded by @code{syssetsignals}	21	## Superseded by @command{syssetsignals}.
22	## @end deftypefn	22	## @end deftypefn
23		23
24	## Author: John Ingram <ingraje@eng.auburn.edu>	24	## Author: John Ingram <ingraje@eng.auburn.edu>




## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8})
##
## Form an arbitrary complex (open or closed loop) system in
## state-space form from several systems. @command{buildssic} can
## easily (despite its cryptic syntax) integrate transfer functions
## from a complex block diagram into a single system with one call.
## This function is especially useful for building open loop
## interconnections for 
## @iftex
## @tex
## $ { \cal H }_\infty $ and $ { \cal H }_2 $
## @end tex
## @end iftex
## @ifinfo
## H-infinity and H-2
## @end ifinfo
## designs or for closing loops with these controllers.
##
## Although this function is general purpose, the use of @command{sysgroup}
## @command{sysmult}, @command{sysconnect} and the like is recommended for
## standard operations since they can handle mixed discrete and continuous
## systems and also the names of inputs, outputs, and states.
##
## The parameters consist of 4 lists that describe the connections
## outputs and inputs and up to 8 systems @var{s1}--@var{s8}.
## Format of the lists:
## @table @var
## @item      clst

## equal to the sum of all inputs of s1-s8.
##
## Example:
## @code{[1 2 -1; 2 1 0]} means that:  new input 1 is old input 1
## + output 2 - output 1, and new input 2 is old input 2
## + output 1. The order of rows is arbitrary.
##
## @item ulst
## if not empty the old inputs in vector @var{ulst} will
## be appended to the outputs. You need this if you
## want to ``pull out'' the input of a system. Elements
## are input numbers of @var{s1}--@var{s8}.
##
## @item olst
## output list, specifiy the outputs of the resulting
## systems. Elements are output numbers of @var{s1}--@var{s8}.
## The numbers are allowed to be negative and may
## appear in any order. An empty matrix means
## all outputs.
##
## @item ilst
## input list, specifiy the inputs of the resulting
## systems. Elements are input numbers of @var{s1}--@var{s8}.
## The numbers are allowed to be negative and may
## appear in any order. An empty matrix means
## all inputs.
## @end table

## @end group
## @end example
##
## The closed loop system @var{GW} can be optained by
## @example
## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K);
## @end example
## @table @var
## @item clst
## 1st row: connect input 1 (@var{G}) with output 2 (@var{K}).
##
## 2nd row: connect input 2 (@var{K}) with negative output 1 (@var{G}).
## @item ulst
## Append input of 2 (@var{K}) to the number of outputs.
## @item olst
## Outputs are output of 1 (@var{G}), 2 (@var{K}) and 
## appended output 3 (from @var{ulst}).
## @item ilst
## The only input is 2 (@var{K}).
## @end table
##
## Here is a real example:

##                          +----+
##     -------------------->| W1 |---> v1
## z   |                    +----+
## ----|-------------+
##     |             |
##     |    +---+    v      +----+
##     *--->| G |--->O--*-->| W2 |---> v2
##     |    +---+       |   +----+

##    u                  y
## @end group
## @end example
## @iftex
## @tex
## $$ { \rm min } \Vert GW_{vz} \Vert _\infty $$  
## @end tex
## @end iftex
## @ifinfo
## @example
## min || GW   ||
##          vz   infty
## @end example
## @end ifinfo
##
## The closed loop system @var{GW} 
## @iftex
## @tex
## from $ [z,~u]^{ \rm T } $ to $ [v_1,~v_2,~y]^{ \rm T } $
## @end tex
## @end iftex
## @ifinfo
## from [z, u]' to [v1, v2, y]' 
## @end ifinfo
## can be obtained by (all @acronym{SISO} systems):
## @example
## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5],
##                [3, 4], G, W1, W2, One);
## @end example
## where ``One'' is a unity gain (auxillary) function with order 0.
## (e.g. @code{One = ugain(1);})
## @end deftypefn





## @deftypefn {Function File} {} c2d (@var{sys}, @var{opt}, @var{t})
## @deftypefnx {Function File} {} c2d (@var{sys}, @var{t})
##
## Converts the system data structure describing:
## @iftex
## @tex
## $$ \dot x = A_c\,x + B_c\,u $$
## @end tex
## @end iftex
## @ifinfo
## @example
## .
## x = Ac x + Bc u
## @end example
## @end ifinfo
## into a discrete time equivalent model:
## @iftex
## @tex
## $$ x_{n+1} = A_d\,x_n + B_d\,u_n $$
## @end tex
## @end iftex
## @ifinfo
## @example
## x[n+1] = Ad x[n] + Bd u[n]
## @end example
## @end ifinfo
## via the matrix exponential or bilinear transform.
##
## @strong{Inputs}
## @table @var
## @item sys

## use the matrix exponential (default)
## @item "bi"
## use the bilinear transformation
## @iftex
## @tex
## $$ s = { 2\,(z-1) \over T\,(z+1) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
##     2(z-1)
## s = -----
##     T(z+1)
## @end example
## @end ifinfo
## FIXME: This option exits with an error if @var{sys} is not purely
## continuous. (The @code{ex} option can handle mixed systems.)
## @item t
## sampling time; required if sys is purely continuous.
##
## If the 2nd argument is not a string, @code{c2d} assumes that
## the 2nd argument is @var{t} and performs appropriate argument checks.
## @item "matched"
## Use the matched pole/zero equivalent transformation (currently only
## works for purely continuous @acronym{SISO} systems).
## @end table
## @item t
## sampling time; required if @var{sys} is purely continuous.
## 
## @strong{Note:} if the second argument is not a string, @code{c2d()}
## assumes that the second argument is @var{t} and performs 
## appropriate argument checks.
## @end table
##
## @strong{Output}
## @table @var
## @item dsys 
## Discrete time equivalent via zero-order hold, sample each @var{t} sec.
## @end table
## @example
## .
## x = Ac x + Bc u
## @end example
## into a discrete time equivalent model
## @example
## x[n+1] = Ad x[n] + Bd u[n]
## @end example
## via the matrix exponential or bilinear transform
##
## This function adds the suffix  @code{_d}
## to the names of the new discrete states.

Lines 19-26 Link Here

(-)octave-2.1.58/scripts/control/system/d2c.m (-5 / +8 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} d2c (@var{sys}, @var{tol})	20	## @deftypefn {Function File} {} d2c (@var{sys}, @var{tol})
21	## @deftypefnx {Function File} {} d2c (@var{sys}, @var{opt})	21	## @deftypefnx {Function File} {} d2c (@var{sys}, @var{opt})
22	## Convert discrete (sub)system to a purely continuous system. Sampling	22	## Convert a discrete (sub)system into a purely continuous one.
23	## time used is @code{sysgettsam(@var{sys})}	23	## The sampling time used is @code{sysgettsam(@var{sys})}.
24	##	24	##
25	## @strong{Inputs}	25	## @strong{Inputs}
26	## @table @var	26	## @table @var
Lines 28-34 Link Here
28	## system data structure with discrete components	28	## system data structure with discrete components
29	## @item tol	29	## @item tol
30	## Scalar value.	30	## Scalar value.
31	## tolerance for convergence of default @code{"log"} option (see below)	31	## Tolerance for convergence of default @code{"log"} option (see below)
32	## @item opt	32	## @item opt
33	## conversion option. Choose from:	33	## conversion option. Choose from:
34	## @table @code	34	## @table @code
Lines 50-57 Link Here
50	## discrete	50	## discrete
51	## @end table	51	## @end table
52	## @end table	52	## @end table
53	## @strong{Outputs} @var{csys} continuous time system (same dimensions and	53	## @strong{Output}
54	## signal names as in @var{sys}).	54	## @table @var
		55	## @item csys
		56	## continuous time system (same dimensions and signal names as in @var{sys}).
		57	## @end table
55	## @end deftypefn	58	## @end deftypefn
56		59
57	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>	60	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>





## -*- texinfo -*-
## @deftypefn {Function File} {} fir2sys (@var{num}, @var{tsam}, @var{inname}, @var{outname})
## construct a system data structure from @acronym{FIR} description
##
## @strong{Inputs}
## @table @var
## @item num
## vector of coefficients 
## of the SISO FIR transfer function
## @ifinfo
## [c0, c1, ..., cn]
## @end ifinfo
## @iftex
## @tex
## $ [c_0, ~ c_1, ~ \ldots, ~ c_n ]$
## @end tex
## @end iftex
## of the @acronym{SISO} @acronym{FIR} transfer function
## @ifinfo
## C(z) = c0 + c1*z^(-1) + c2*z^(-2) + ... + cn*z^(-n)
## @end ifinfo
## @iftex
## @tex
## $$ C(z) = c_0 + c_1\,z^{-1} + c_2\,z^{-2} + \ldots + c_n\,z^{-n} $$
## @end tex
## @end iftex
##

## name of output signal; may be a string or a list with a single entry.
## @end table
##
## @strong{Output}
## @table @var
## @item sys
## system data structure
## @end table
##
## @strong{Example}
## @example
## octave:1> sys = fir2sys([1 -1 2 4],0.342,\
## > "A/D input","filter output");
## octave:2> sysout(sys)
## Input(s)
##         1: A/D input

Lines 17-27 Link Here

(-)octave-2.1.58/scripts/control/system/is_abcd.m (-2 / +2 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} is_abcd (@var{a}, @var{b}, @var{c}, @var{d})	20	## @deftypefn {Function File} {@var{retval} =} is_abcd (@var{a}, @var{b}, @var{c}, @var{d})
21	## Returns @var{retval} = 1 if the dimensions of @var{a}, @var{b},	21	## Returns @var{retval} = 1 if the dimensions of @var{a}, @var{b},
22	## @var{c}, @var{d} are compatible, otherwise @var{retval} = 0 with an	22	## @var{c}, @var{d} are compatible, otherwise @var{retval} = 0 with an
23	## appropriate diagnostic message printed to the screen. The matrices	23	## appropriate diagnostic message printed to the screen. The matrices
24	## b, c, or d may be omitted.	24	## @var{b}, @var{c}, or @var{d} may be omitted.
25	## @end deftypefn	25	## @end deftypefn
26	## @seealso{abcddim}	26	## @seealso{abcddim}
27		27

Lines 38-45 Link Here

(-)octave-2.1.58/scripts/control/system/is_controllable.m (-2 / +2 lines)
38	## Logical flag; returns true (1) if the system @var{sys} or the	38	## Logical flag; returns true (1) if the system @var{sys} or the
39	## pair (@var{a}, @var{b}) is controllable, whichever was passed as input	39	## pair (@var{a}, @var{b}) is controllable, whichever was passed as input
40	## arguments.	40	## arguments.
41	## @item U	41	## @item u
42	## U is an orthogonal basis of the controllable subspace.	42	## @var{u} is an orthogonal basis of the controllable subspace.
43	## @end table	43	## @end table
44	##	44	##
45	## @strong{Method}	45	## @strong{Method}

Lines 23-31 Link Here

(-)octave-2.1.58/scripts/control/system/is_detectable.m (-2 / +2 lines)
23	##	23	##
24	## Returns 1 if the system @var{a} or the pair (@var{a}, @var{c}) is	24	## Returns 1 if the system @var{a} or the pair (@var{a}, @var{c}) is
25	## detectable, 0 if not, and -1 if the system has unobservable modes at the	25	## detectable, 0 if not, and -1 if the system has unobservable modes at the
26	## imaginary axis (unit circle for discrete-time systems)	26	## imaginary axis (unit circle for discrete-time systems).
27	##	27	##
28	## @strong{See} @code{is_stabilizable} for detailed description of	28	## @strong{See} @command{is_stabilizable} for detailed description of
29	## arguments and computational method.	29	## arguments and computational method.
30	##	30	##
31	##	31	##




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{digital} =} is_digital (@var{sys}, @var{eflg})
## Return nonzero if system is digital.
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure.
## @item eflg
## When equal to 0 (default value), exits with an error if the system 
## is mixed (continuous and discrete components); when equal to 1, print
## a warning if the system is mixed (continuous and discrete); when equal
## to 2, operate silently.
## @end table
##
## @strong{Output}
## @table @var
## @item digital
## When equal to 0, the system is purely continuous; when equal to 1, the
## system is purely discrete; when equal to -1, the system is mixed continuous 
## and discrete.
## @end table
## Exits with an error if @var{sys} is a mixed (continuous and discrete) system.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>




## @deftypefnx {Function File} {[@var{retval}, @var{u}] =} is_observable (@var{sys}, @var{tol})
## Logical check for system observability.
##
## Default: tol = @code{tol = 10*norm(a,'fro')*eps}
##
## Returns 1 if the system @var{sys} or the pair (@var{a}, @var{c}) is
## observable, 0 if not.
##
## See @command{is_controllable} for detailed description of arguments
## and default values.
## @end deftypefn
## @seealso{size, rows, columns, length, ismatrix, isscalar, and isvector}

Lines 19-25 Link Here

(-)octave-2.1.58/scripts/control/system/is_sample.m (-1 / +1 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} is_sample (@var{ts})	20	## @deftypefn {Function File} {} is_sample (@var{ts})
21	## Return true if @var{ts} is a valid sampling time	21	## Return true if @var{ts} is a valid sampling time
22	## (real,scalar, > 0)	22	## (real, scalar, > 0).
23	## @end deftypefn	23	## @end deftypefn
24		24
25	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	25	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 18-24 Link Here

(-)octave-2.1.58/scripts/control/system/is_siso.m (-1 / +1 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} is_siso (@var{sys})	20	## @deftypefn {Function File} {} is_siso (@var{sys})
21	## return nonzero if the system data structure	21	## Returns nonzero if the system data structure
22	## @var{sys} is single-input, single-output.	22	## @var{sys} is single-input, single-output.
23	## @end deftypefn	23	## @end deftypefn
24		24




## Copyright (C) 1998 Kai P. Mueller.
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it

## @deftypefnx {Function File} {@var{retval} =} is_stabilizable (@var{a}, @var{b}, @var{tol}, @var{dflg})
## Logical check for system stabilizability (i.e., all unstable modes are controllable). 
## Returns 1 if the system is stabilizable, 0 if the the system is not stabilizable, -1 
## if the system has non stabilizable modes at the imaginary axis (unit circle for 
## discrete-time systems.
##
## Test for stabilizability is performed via Hautus Lemma. If @var{dflg}!=0 assume that 
## discrete-time matrices (a,b) are supplied.
##
## Test for stabilizability is performed via Hautus Lemma. If 
## @iftex
## @tex
## @var{dflg}$\neq$0
## @end tex
## @end iftex
## @ifinfo 
## @var{dflg}!=0
## @end ifinfo
## assume that discrete-time matrices (a,b) are supplied.
## @end deftypefn
## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector
## is_observable, is_stabilizable, is_detectable}

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1993




## @strong{Inputs}
## @table @var
## @item  tol
## is a roundoff parameter, set to 200*@code{eps} if omitted.
## @item dflg
## Digital system flag (not required for system data structure):
## @table @code
## @item @var{dflg} != 0
## stable if eig(a) is in the unit circle
##
## @item @var{dflg} == 0
## stable if eig(a) is in the open LHP (default)
## @end table
## @end table
## @end deftypefn




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{sys} =} jet707 ()
## Creates a linearized state-space model of a Boeing 707-321 aircraft
## at @var{v}=80 m/s 
## @iftex
## @tex
## ($M = 0.26$, $G_{a0} = -3^{\circ}$, ${\alpha}_0 = 4^{\circ}$, ${\kappa}= 50^{\circ}$).
## @end tex
## @end iftex
## @ifinfo
## (@var{M} = 0.26, @var{Ga0} = -3 deg, @var{alpha0} = 4 deg, @var{kappa} = 50 deg).
## @end ifinfo
##
## System inputs: (1) thrust and (2) elevator angle.
##
## System outputs:  (1) airspeed and (2) pitch angle.
##
## @strong{Reference}: R. Brockhaus: @cite{Flugregelung} (Flight Control), Springer, 1994.
## @end deftypefn
## @seealso{ord2}


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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} moddemo (@var{inputs})	20	## @deftypefn {Function File} {} moddemo (@var{inputs})
21	## Octave Controls toolbox demo: Model Manipulations demo	21	## Octave Control toolbox demo: Model Manipulations demo.
22	## @end deftypefn	22	## @end deftypefn
23		23
24	## Author: David Clem	24	## Author: David Clem




## -*- texinfo -*-
## @deftypefn {Function File} {} ord2 (@var{nfreq}, @var{damp}, @var{gain})
## Creates a continuous 2nd order system with parameters:
##
## @strong{Inputs}
## @table @var
## @item nfreq

## This is steady state value only for damp > 0.
## gain is assumed to be 1.0 if ommitted.
## @end table
##
## @strong{Output}
## @table @var
## @item outsys
## system data structure has representation with 
## @ifinfo
## @math{w = 2 * pi * nfreq}:
## @end ifinfo
## @iftex
## @tex
## $ w = 2 \, \pi \, f $:
## @end tex
## @end iftex
## @example
## @group
##     /                                        \
##     | / -2w*damp -w \  / w \                 |
## G = | |             |, |   |, [ 0  gain ], 0 |
##     | \   w       0 /  \ 0 /                 |
##     \                                        /
## @end group
## @end example
## @end table
## @strong{See also} @command{jet707} (@acronym{MIMO} example, Boeing 707-321
## aircraft model)
## @end deftypefn


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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} parallel (@var{asys}, @var{bsys})	20	## @deftypefn {Function File} {@var{ksys} =} parallel (@var{asys}, @var{bsys})
21	## Forms the parallel connection of two systems.	21	## Forms the parallel connection of two systems.
22	##	22	##
23	## ____________________	23	## @example
24	## \| ________ \|	24	## @group
		25	## --------------------
		26	## \| -------- \|
25	## u ----->\|----> \| asys \|--->\|----> y1	27	## u ----->\|----> \| asys \|--->\|----> y1
26	## \| \| -------- \|	28	## \| \| -------- \|
27	## \| \| ________ \|	29	## \| \| -------- \|
28	## \|--->\|----> \| bsys \|--->\|----> y2	30	## \|--->\|----> \| bsys \|--->\|----> y2
29	## \| -------- \|	31	## \| -------- \|
30	## --------------------	32	## --------------------
31	## ksys	33	## ksys
		34	## @end group
		35	## @end example
32	## @end deftypefn	36	## @end deftypefn
33		37
34	## Author: David Clem	38	## Author: David Clem

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19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist})	20	## @deftypefn {Function File} {} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist})
21	## Create system structure from state-space data. May be continous,	21	## Create system structure from state-space data. May be continous,
22	## discrete, or mixed (sampeled-data)	22	## discrete, or mixed (sampled data)
23	##	23	##
24	## @strong{Inputs}	24	## @strong{Inputs}
25	## @table @var	25	## @table @var

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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} ss2tf (@var{inputs})	20	## @deftypefn {Function File} {[@var{num}, @var{den}] =} ss2tf (@var{a}, @var{b}, @var{c}, @var{d})
21	## @format
22	## [num,den] = ss2tf(a,b,c,d)
23	## Conversion from tranfer function to state-space.	21	## Conversion from tranfer function to state-space.
24	## The state space system	22	## The state space system:
		23	## @iftex
		24	## @tex
		25	## $$ \dot x = A\,x + B\,u $$
		26	## $$ y = C\,x + D\,u $$
		27	## @end tex
		28	## @end iftex
		29	## @ifinfo
		30	## @example
25	## .	31	## .
26	## x = Ax + Bu	32	## x = Ax + Bu
27	## y = Cx + Du	33	## y = Cx + Du
		34	## @end example
		35	## @end ifinfo
28	##	36	##
29	## is converted to a transfer function	37	## is converted to a transfer function:
		38	## @iftex
		39	## @tex
		40	## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$
		41	## @end tex
		42	## @end iftex
		43	## @ifinfo
		44	## @example
30	##	45	##
31	## num(s)	46	## num(s)
32	## G(s)=-------	47	## G(s)=-------
33	## den(s)	48	## den(s)
		49	## @end example
		50	## @end ifinfo
34	##	51	##
35	## used internally in system data structure format manipulations	52	## used internally in system data structure format manipulations.
36	## @end format
37	## @end deftypefn	53	## @end deftypefn
38		54
39	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>	55	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{pol}, @var{zer}, @var{k}] =} ss2zp (@var{a}, @var{b}, @var{c}, @var{d})
## Converts a state space representation to a set of poles and zeros;
## @var{k} is a gain associated with the zeros.
##
## Used internally in system data structure format manipulations.
## system (a,b,c,d).  K is a gain associated with the zeros.
##
## used internally in system data structure format manipulations
## @end format
## @end deftypefn

## Author: David Clem

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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist})	20	## @deftypefn {Function File} {@var{outsys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist})
21	## Create system structure from state-space data. May be continous,	21	## Create system structure from state-space data. May be continous,
22	## discrete, or mixed (sampeled-data)	22	## discrete, or mixed (sampled data)
23	##	23	##
24	## @strong{Inputs}	24	## @strong{Inputs}
25	## @table @var	25	## @table @var
Lines 75-82 Link Here
75	## @code{sys2ss} returns a vector @var{yd} where	75	## @code{sys2ss} returns a vector @var{yd} where
76	## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0.	76	## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0.
77	##	77	##
78	## @strong{Outputs}	78	## @strong{Output}
79	## @var{outsys} = system data structure	79	## @table @var
		80	## @item outsys
		81	## system data structure
		82	## @end table
80	##	83	##
81	## @strong{System partitioning}	84	## @strong{System partitioning}
82	##	85	##





## -*- texinfo -*-
## @deftypefn {Function File} {} starp (@var{P}, @var{K}, @var{ny}, @var{nu})
## @format
##
## Redheffer star product or upper/lower LFT, respectively.
## @example
## @group
##
##                +-------+
##      --------->|       |--------->

##                |   K   |
##      --------->|       |--------->
##                +-------+
## @end group
## @end example
## If @var{ny} and @var{nu} ``consume'' all inputs and outputs of
## @var{K} then the result is a lower fractional transformation. 
## If @var{ny} and @var{nu} ``consume'' all inputs and outputs of 
## @var{P} then the result is an upper fractional transformation.
##
## @var{ny} and/or @var{nu} may be negative (i.e. negative feedback).
## is a lower fractional transformation. If ny and nu "consume" all
## inputs and outputs of P then the result is an upper fractional
## transformation.
##
## ny and/or nu may be negative (= negative feedback)
## @end format
## @end deftypefn

## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>

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19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{c}, @var{tsam}, @var{input}, @var{output}] =} sys2fir (@var{sys})	20	## @deftypefn {Function File} {[@var{c}, @var{tsam}, @var{input}, @var{output}] =} sys2fir (@var{sys})
21	##	21	##
22	## Extract FIR data from system data structure; see fir2sys for	22	## Extract @acronym{FIR} data from system data structure; see @command{fir2sys} for
23	## parameter descriptions.	23	## parameter descriptions.
24	## @end deftypefn	24	## @end deftypefn
25	## @seealso{fir2sys}	25	## @seealso{fir2sys}




## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{yd}] =} sys2ss (@var{sys})
## Extract state space representation from system data structure.
##
## @strong{Input}
## @table @var
## @item sys
## System data structure.
## @end table
##
## @strong{Outputs}
## @table @var

## @itemx b
## @itemx c
## @itemx d
## State space matrices for @var{sys}.
##
## @item tsam
## Sampling time of @var{sys} (0 if continuous).
##
## @item n
## @itemx nz
## Number of continuous, discrete states (discrete states come
## last in state vector @var{x}).
##
## @item stname
## @itemx inname
## @itemx outname
## Signal names (lists of strings);  names of states,
## inputs, and outputs, respectively.
##
## @item yd
## Binary vector; @var{yd}(@var{ii}) is 1 if output @var{y}(@var{ii})
## is discrete (sampled); otherwise  @var{yd}(@var{ii}) is 0.
##
## @end table
## A warning massage is printed if the system is a mixed
## continuous and discrete system.
##
## @strong{Example}
## @example

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18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{num}, @var{den}, @var{tsam}, @var{inname}, @var{outname}] =} sys2tf (@var{sys})	20	## @deftypefn {Function File} {[@var{num}, @var{den}, @var{tsam}, @var{inname}, @var{outname}] =} sys2tf (@var{sys})
21	## Extract transfer function data from a system data structure	21	## Extract transfer function data from a system data structure.
22	##	22	##
23	## See tf for parameter descriptions.	23	## See @command{tf} for parameter descriptions.
24	##	24	##
25	## @strong{Example}	25	## @strong{Example}
26	## @example	26	## @example

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19	## -- texinfo --	19	## -- texinfo --
20	##@deftypefn {Function File} {[@var{zer}, @var{pol}, @var{k}, @var{tsam}, @var{inname}, @var{outname}] =} sys2zp (@var{sys})	20	##@deftypefn {Function File} {[@var{zer}, @var{pol}, @var{k}, @var{tsam}, @var{inname}, @var{outname}] =} sys2zp (@var{sys})
21	## Extract zero/pole/leading coefficient information from a system data	21	## Extract zero/pole/leading coefficient information from a system data
22	## structure	22	## structure.
23	##	23	##
24	## See zp for parameter descriptions.	24	## See @command{zp} for parameter descriptions.
25	##	25	##
26	## @strong{Example}	26	## @strong{Example}
27	## @example	27	## @example




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{sys} =} sysappend (@var{syst}, @var{b}, @var{c}, @var{d}, @var{outname}, @var{inname}, @var{yd})
## appends new inputs and/or outputs to a system
##
## @strong{Inputs}
## @table @var
## @item syst
## system data structure
##
## @item b

## @math{yd(ii)=1} indicates a discrete output.
## @end table
##
## @strong{Outputs}
## @table @var
## @item sys
## @example
## @group
##    sys.b := [syst.b , b]
##    sys.c := [syst.c  ]
##             [ c     ]
##    sys.d := [syst.d | D12 ]
##             [ D21   | D22 ]
## @end group
## @end example
## where @math{D12}, @math{D21}, and @math{D22} are the appropriate dimensioned

##      the new inputs and outputs are be assigned default names.
## @item @var{yd} is a binary vector of length rows(c) that indicates
##      continuous/sampled outputs.  Default value for @var{yd} is:
## @itemize @minus
## @item @var{sys} is continuous or mixed
## @var{yd} = @code{zeros(1,rows(c))}
##
## @item @var{sys} is discrete
## @var{yd} = @code{ones(1,rows(c))}
## @end itemize
## @end itemize
## @end table
## @end deftypefn

## Author: John Ingram <ingraje@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{clsys} =} sysconnect (@var{sys}, @var{out_idx}, @var{in_idx}, @var{order}, @var{tol})
## Close the loop from specified outputs to respective specified inputs
##
## @strong{Inputs}
## @table @var
## @item   sys
## System data structure.
## @item   out_idx
## @itemx  in_idx
## Names or indices of signals to connect (see @code{sysidx}).
## The output specified by @math{out_idx(ii)} is connected to the input
## specified by @math{in_idx(ii)}.
## @item   order
## logical flag (default = 0)
## @table @code
## @item        0
## Leave inputs and outputs in their original order.
## @item        1
## Permute inputs and outputs to the order shown in the diagram below.
## @end table
## @item     tol
## Tolerance for singularities in algebraic loops, default: 200@code{eps}.
## @end table
##
## @strong{Outputs}
## @table @var
## @item clsys
## Resulting closed loop system.
## @end table
##
## @strong{Method}
##
## @code{sysconnect} internally permutes selected inputs, outputs as shown
## below, closes the loop, and then permutes inputs and outputs back to their
## original order
## @example
## @group
##                  --------------------
##  u_1       ----->|                  |----> y_1
##                  |        sys       |
##          old u_2 |                  |
## u_2* ---->(+)--->|                  |----->y_2
## (in_idx)   ^     --------------------    | (out_idx)
##            |                             |
##            -------------------------------
## @end group

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20	## @deftypefn {Function File} {[@var{csys}, @var{acd}, @var{ccd}] =} syscont (@var{sys})	20	## @deftypefn {Function File} {[@var{csys}, @var{acd}, @var{ccd}] =} syscont (@var{sys})
21	## Extract the purely continuous subsystem of an input system.	21	## Extract the purely continuous subsystem of an input system.
22	##	22	##
23	## @strong{Inputs}	23	## @strong{Input}
24	## @var{sys} is a system data structure	24	## @table @var
		25	## @item sys
		26	## system data structure.
		27	## @end table
25	##	28	##
26	## @strong{Outputs}	29	## @strong{Outputs}
27	## @table @var	30	## @table @var




## -*- texinfo -*-
## @deftypefn {Function File} {[@var{dsys}, @var{adc}, @var{cdc}] =} sysdisc (@var{sys})
##
## @strong{Input}
## @table @var
## @item sys
## System data structure.
## @end table
##
## @strong{Outputs}
## @table @var
## @item dsys
## Purely discrete portion of sys (returned empty if there is
## no purely discrete path from inputs to outputs).
## @item    adc
## @itemx   cdc
## Connections from continuous states to discrete states and discrete.
## outputs, respectively.
## @end table
## @end deftypefn




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{retsys} =} sysdup (@var{asys}, @var{out_idx}, @var{in_idx})
## Duplicate specified input/output connections of a system
##
## @strong{Inputs}

## duplicates are made of @code{y(out_idx(ii))} and @code{u(in_idx(ii))}.
## @end table
##
## @strong{Output}
## @table @var
## @item retsys
## Resulting closed loop system:
## duplicated i/o names are appended with a @code{"+"} suffix.
## @end table
##
## @strong{Method}
##
## @code{sysdup} creates copies of selected inputs and outputs as
## shown below.  @var{u1}, @var{y1} is the set of original inputs/outputs, and
## @var{u2}, @var{y2} is the set of duplicated inputs/outputs in the order 
## specified in @var{in_idx}, @var{out_idx}, respectively
## @example
## @group
##           ____________________
## u1  ----->|                  |----> y1
##           |       asys       |
## u2 ------>|                  |----->y2
## (in_idx)  -------------------- (out_idx)
## @end group
## @end example
## @end deftypefn




##
## @strong{Outputs}
## @table @bullet
## @item If @var{sigid} is not specified:
## @table @var
## @item stname
## @itemx inname
## @itemx outname
## signal names (cell array of strings);  names of states,
## inputs, and outputs, respectively.
## @item yd
## binary vector; @var{yd}(@var{ii}) is nonzero if output @var{ii} is
## discrete.
## @end table
##
## @item If @var{sigid} is specified but @var{signum} is not specified:
## @table @code
## @item sigid="in"
## @var{siglist} is set to the cell array of input names.
##
## @item sigid="out"
## @var{siglist} is set to the cell array of output names.
##
## @item sigid="st"
## @var{siglist} is set to the cell array of state names.
##
## stage signals
## @item sigid="yd"

##
## @end table
##
## @item If the first three input arguments are specified:
## @var{signame} is a cell array of the specified signal names (@var{sigid} is 
## @code{"in"}, @code{"out"}, or @code{"st"}), or else the logical flag
## indicating whether output(s) @var{signum} is(are) discrete (@var{sigval}=1)
## or continuous (@var{sigval}=0).
## @end table

## @strong{Examples} (From @code{sysrepdemo})
## @example
## octave> sys=ss(rand(4),rand(4,2),rand(3,4));
## octave># get all signal names
## octave> [Ast,Ain,Aout,Ayd] = sysgetsignals(sys)
## Ast =
## (
##   [1] = x_1

## Ayd =
##
##   0  0  0
## octave> # get only input signal names:
## octave> Ain = sysgetsignals(sys,"in")
## Ain =
## (
##   [1] = u_1
##   [2] = u_2
## )
## octave> # get name of output 2 (in cell array):
## octave> Aout = sysgetsignals(sys,"out",2)
## Aout =
## (
##   [1] = y_2
## )
## octave> # get name of output 2 (as string):
## octave> Aout = sysgetsignals(sys,"out",2,1)
## Aout = y_2
## @end example
## @end deftypefn

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20	## @deftypefn {Function File} {} sysgettype (@var{sys})	20	## @deftypefn {Function File} {} sysgettype (@var{sys})
21	## return the initial system type of the system	21	## return the initial system type of the system
22	##	22	##
23	## @strong{Inputs}	23	## @strong{Input}
24	## @var{sys}: system data structure	24	## @table @var
		25	## @item sys
		26	## System data structure.
		27	## @end table
25	##	28	##
26	## @strong{Outputs}	29	## @strong{Output}
27	## @var{systype}: string indicating how the structure was initially	30	## @table @var
28	## constructed:	31	## @item systype
29	## values: @code{"ss"}, @code{"zp"}, or @code{"tf"}	32	## String indicating how the structure was initially
		33	## constructed. Values: @code{"ss"}, @code{"zp"}, or @code{"tf"}.
		34	## @end table
30	##	35	##
31	## FIR initialized systems return @code{systype="tf"}.	36	## @acronym{FIR} initialized systems return @code{systype="tf"}.
32	## @end deftypefn	37	## @end deftypefn
33		38
34	function systype = sysgettype (sys)	39	function systype = sysgettype (sys)

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17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} sysgroup (@var{asys}, @var{bsys})	20	## @deftypefn {Function File} {@var{sys} =} sysgroup (@var{asys}, @var{bsys})
21	## Combines two systems into a single system	21	## Combines two systems into a single system.
22	##	22	##
23	## @strong{Inputs}	23	## @strong{Inputs}
24	## @var{asys}, @var{bsys}: system data structures	24	## @table @var
		25	## @item asys
		26	## @itemx bsys
		27	## System data structures.
		28	## @end table
25	##	29	##
26	## @strong{Outputs}	30	## @strong{Output}
		31	## @table @var
		32	## @item sys
27	## @math{sys = @r{block diag}(asys,bsys)}	33	## @math{sys = @r{block diag}(asys,bsys)}
		34	## @end table
28	## @example	35	## @example
29	## @group	36	## @group
30	## __________________	37	## __________________
Lines 39-46 Link Here
39	## @end group	46	## @end group
40	## @end example	47	## @end example
41	## The function also rearranges the internal state-space realization of @var{sys}	48	## The function also rearranges the internal state-space realization of @var{sys}
42	## so that the	49	## so that the continuous states come first and the discrete states come last.
43	## continuous states come first and the discrete states come last.
44	## If there are duplicate names, the second name has a unique suffix appended	50	## If there are duplicate names, the second name has a unique suffix appended
45	## on to the end of the name.	51	## on to the end of the name.
46	## @end deftypefn	52	## @end deftypefn





## -*- texinfo -*-
## @deftypefn {Function File} {[@var{retsys}, @var{nc}, @var{no}] =} sysmin (@var{sys}, @var{flg})
## Returns a minimal (or reduced order) system
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure
## @item flg
## When equal to 0 (default value), returns minimal system,
## in which state names are lost; when equal to 1, returns system 
## with physical states removed that are either uncontrollable or 
## unobservable (cannot reduce further without discarding physical
## meaning of states).
## @end table
## @strong{Outputs}
## @table @var
## @item retsys
## Returned system.
## @item nc
## Number of controllable states in the returned system.
## @item no
## Number of observable states in the returned system.
## @item cflg
## @code{is_controllable(retsys)}.
## @item oflg
## @code{is_observable(retsys)}.
## @end table
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{sys} =} sysmult (@var{Asys}, @var{Bsys})
## Compute @math{sys = Asys*Bsys} (series connection):
## @example
## @group
## u   ----------     ----------
## --->|  Bsys  |---->|  Asys  |--->
##     ----------     ----------
## @end group
## @end example
## A warning occurs if there is direct feed-through from an input 
## or a continuous state of @var{Bsys}, through a discrete output 
## of @var{Bsys}, to a continuous state or output in @var{Asys}
## (system data structure does not recognize discrete inputs).
## @end deftypefn





## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{retsys} =} sysprune (@var{asys}, @var{out_idx}, @var{in_idx})
## Extract specified inputs/outputs from a system
##
## @strong{Inputs}

## system data structure
## @item out_idx
## @itemx in_idx
##
## Indices or signal names of the outputs and inputs to be kept in the returned
## system; remaining connections are ``pruned'' off.
## May select as [] (empty matrix) to specify all outputs/inputs.
##
## @example

##
## @end table
##
## @strong{Output}
## @table @var
## @item retsys
## Resulting system.
## @end table
## @example
## @group
##            ____________________

Lines 17-30 Link Here

(-)octave-2.1.58/scripts/control/system/sysreorder.m (-4 / +12 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} sysreorder (@var{vlen}, @var{list})	20	## @deftypefn {Function File} {@var{pv} =} sysreorder (@var{vlen}, @var{list})
21	##	21	##
22	## @strong{Inputs}	22	## @strong{Inputs}
23	## @var{vlen}=vector length, @var{list}= a subset of @code{[1:vlen]},	23	## @table @var
		24	## @item vlen
		25	## Vector length.
		26	## @item list
		27	## A subset of @code{[1:vlen]}.
		28	## @end table
24	##	29	##
25	## @strong{Outputs}	30	## @strong{Output}
26	## @var{pv}: a permutation vector to order elements of @code{[1:vlen]} in	31	## @table @var
		32	## @item pv
		33	## A permutation vector to order elements of @code{[1:vlen]} in
27	## @code{list} to the end of a vector.	34	## @code{list} to the end of a vector.
		35	## @end table
28	##	36	##
29	## Used internally by @code{sysconnect} to permute vector elements to their	37	## Used internally by @code{sysconnect} to permute vector elements to their
30	## desired locations.	38	## desired locations.




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{retsys} =} sysscale (@var{sys}, @var{outscale}, @var{inscale}, @var{outname}, @var{inname})
## scale inputs/outputs of a system.
##
## @strong{Inputs}
## @table @var
## @item sys
## Structured system.
## @item outscale
## @itemx inscale
## Constant matrices of appropriate dimension.
## @item outname
## @itemx inname
## Lists of strings with the names of respectively outputs and inputs.
## @end table
##
## @strong{Output}
## @table @var
## @item retsys
## resulting open loop system:
## @example
##       -----------    -------    -----------
## u --->| inscale |--->| sys |--->| outscale |---> y
##       -----------    -------    -----------
## @end example
## @end table
## If the input names and output names (each a list of strings)
## are not given and the scaling matrices
## are not square, then default names will be given to the inputs and/or




## -*- texinfo -*-
## @deftypefn {Function File} {} syssetsignals (@var{sys}, @var{opt}, @var{names}, @var{sig_idx})
## change the names of selected inputs, outputs and states.
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure.
##
## @item opt
## Change default name (output).
##
## @table @code
## @item "out"
## Change selected output names.
## @item "in"
## Change selected input names.
## @item "st"
## Change selected state names.
## @item "yd"
## Change selected outputs from discrete to continuous or
## from continuous to discrete.
## @end table
##
## @item names
## @table @code
## @item opt = "out", "in", "st"
## string or string array containing desired signal names or values.
## @item opt = "yd"
## To desired output continuous/discrete flag.

##
## Default: replace entire cell array of names/entire yd vector.
## @end table
##
## @strong{Outputs}
## @table @var
## @item retsys
## @var{sys} with appropriate signal names changed
## (or @var{yd} values, where appropriate).
## @end table
##
## @strong{Example}
## @example




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{sys} =} syssub (@var{Gsys}, @var{Hsys})
## Return @math{sys = Gsys - Hsys}.
##
## @strong{Method}
##
## @var{Gsys} and @var{Hsys} are connected in parallel.
## The input vector is connected to both systems; the outputs are
## subtracted.  Returned system names are those of @var{Gsys}.
## @example
## @group
##          +--------+
##     +--->|  Gsys  |---+
##     |    +--------+   |
##     |                +|
## u --+                (_)--> y
##     |                -|
##     |    +--------+   |
##     +--->|  Hsys  |---+
##          +--------+
## @end group
## @end example

Lines 39-48 Link Here

(-)octave-2.1.58/scripts/control/system/sysupdate.m (-3 / +6 lines)
39	## @end table	39	## @end table
40	##	40	##
41	## @strong{Outputs}	41	## @strong{Outputs}
42	## @var{retsys}: contains union of data in sys and requested data.	42	## @table @var
43	## If requested data in sys is already up to date then retsys=sys.	43	## @item retsys
		44	## Contains union of data in sys and requested data.
		45	## If requested data in @var{sys} is already up to date then @var{retsys}=@var{sys}.
		46	## @end table
44	##	47	##
45	## Conversion to @code{tf} or @code{zp} exits with an error if the system is	48	## Conversion to @command{tf} or @command{zp} exits with an error if the system is
46	## mixed continuous/digital.	49	## mixed continuous/digital.
47	## @end deftypefn	50	## @end deftypefn
48	## @seealso{tf, ss, zp, sysout, sys2ss, sys2tf, and sys2zp}	51	## @seealso{tf, ss, zp, sysout, sys2ss, sys2tf, and sys2zp}




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} tf2ss (@var{num}, @var{den})
## @format
## Conversion from tranfer function to state-space.
## The state space system:
## @iftex
## @tex
## $$ \dot x = A\,x + B\,u $$
## $$ y = C\,x + D\,u $$
## @end tex
## @end iftex
## @ifinfo
## @example
##       .
##       x = Ax + Bu
##       y = Cx + Du
## @end example
## @end ifinfo
## is obtained from a transfer function:
## @iftex
## @tex
## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
##                 num(s)
##           G(s)=-------
##                 den(s)
## @end example
## @end ifinfo
##
## The vector @var{den} must contain only one row, whereas the vector 
## @var{num} may contain as many rows as there are outputs @var{y} of 
## the system. The state space system matrices obtained from this function 
## will be in controllable canonical form as described in @cite{Modern Control 
## Theory}, (Brogan, 1991).
## [Brogan, 1991].
##
##
## @end format
## @end deftypefn

## Author: R. Bruce Tenison <btenison@eng.auburn.edu>





## -*- texinfo -*-
## @deftypefn {Function File} {} tf2sys (@var{num}, @var{den}, @var{tsam}, @var{inname}, @var{outname})
## Build system data structure from transfer function format data.
##
## @strong{Inputs}
## @table @var
## @item  num
## @itemx den
## Coefficients of numerator/denominator polynomials.
## @item tsam
## Sampling interval; default: 0 (continuous time).
## @item inname
## @itemx outname
## Input/output signal names; may be a string or cell array with a single string
## entry.
## @end table
##
## @strong{Output}
## @table @var
## @item sys
## System data structure.
## @end table
##
## @strong{Example}
## @example




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{zer}, @var{pol}, @var{k}] =} tf2zp (@var{num}, @var{den})
## Converts transfer functions to poles-and-zero representations.
##
## Returns the zeros and poles of the @acronym{SISO} system defined 
## by @var{num}/@var{den}.
## @var{k} is a gain associated with the system zeros.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 20-27 Link Here

(-)octave-2.1.58/scripts/control/system/ugain.m (-2 / +2 lines)
20	## @deftypefn {Function File} {} ugain (@var{n})	20	## @deftypefn {Function File} {} ugain (@var{n})
21	## Creates a system with unity gain, no states.	21	## Creates a system with unity gain, no states.
22	## This trivial system is sometimes needed to create arbitrary	22	## This trivial system is sometimes needed to create arbitrary
23	## complex systems from simple systems with buildssic.	23	## complex systems from simple systems with @command{buildssic}.
24	## Watch out if you are forming sampled systems since "ugain"	24	## Watch out if you are forming sampled systems since @command{ugain}
25	## does not contain a sampling period.	25	## does not contain a sampling period.
26	## @end deftypefn	26	## @end deftypefn
27	## @seealso{hinfdemo and jet707}	27	## @seealso{hinfdemo and jet707}




## -*- texinfo -*-
## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}] =} zp2ss (@var{zer}, @var{pol}, @var{k})
## Conversion from zero / pole to state space.
##
## @strong{Inputs}
## @table @var
## @item zer
## @itemx pol
## Vectors of (possibly) complex poles and zeros of a transfer
## function. Complex values must come in conjugate pairs
## (i.e., @math{x+jy} in @var{zer} means that @math{x-jy} is also in @var{zer}).
## The number of zeros must not exceed the number of poles.
## @item k
## Real scalar (leading coefficient).
## @end table
##
## @strong{Outputs}
## @table @var
## @item @var{a}
## @itemx @var{b}
## @itemx @var{c}
## @itemx @var{d}
## The state space system, in the form:
## @iftex
## @tex
## $$ \dot x = A\,x + B\,u $$
## $$ y = C\,x + D\,u $$
## @end tex
## @end iftex
## @ifinfo
## @example
##      .
##      x = Ax + Bu
##      y = Cx + Du
## @end example
## @end ifinfo
## @end table
## The vectors @samp{zer} and
## @samp{pol} may either be row or column vectors.  Each zero and pole that
## has an imaginary part must have a conjugate in the list.
## The number of zeros must not exceed the number of poles.
## @samp{k} is @code{zp}-form leading coefficient.
## @end deftypefn

## Author: David Clem




## @strong{Inputs}
## @table @var
## @item   zer
## Vector of system zeros.
## @item   pol
## Vector of system poles.
## @item   k
## Scalar leading coefficient.
## @item   tsam
## Sampling period; default: 0 (continuous system).
## @item   inname
## @itemx  outname
## Input/output signal names (lists of strings).
## @end table
##
## @strong{Output}
## @table @var
## @item sys
## System data structure.
## @end table
##
## @strong{Example}
## @example




## -*- texinfo -*-
## @deftypefn {Function File} {[@var{num}, @var{den}] =} zp2tf (@var{zer}, @var{pol}, @var{k})
## Converts zeros / poles to a transfer function.
##
## @strong{Inputs}
## @table @var
## @item zer
## @itemx pol
## Vectors of (possibly complex) poles and zeros of a transfer
## function.  Complex values must appear in conjugate pairs.
## @item k
## Real scalar (leading coefficient).
## @end table
## @code{[num,den] = zp2tf(zer,pol,k)} forms the transfer function
## @code{num/den} from the vectors of poles and zeros.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 18-32 Link Here

(-)octave-2.1.58/scripts/control/util/axis2dlim.m (-7 / +14 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn{Function File} {} axis2dlim (@var{axdata})	20	## @deftypefn{Function File} {} axis2dlim (@var{axdata})
21	## determine axis limits for 2-d data(column vectors); leaves a 10% margin	21	## Determine axis limits for 2-D data (column vectors); leaves a 10%
22	## around the plots.	22	## margin around the plots.
23	## puts in margins of +/- 0.1 if data is one dimensional (or a single point)	23	## Inserts margins of +/- 0.1 if data is one-dimensional
		24	## (or a single point).
24	##	25	##
25	## @strong{Inputs}	26	## @strong{Input}
26	## @var{axdata} nx2 matrix of data [x,y]	27	## @table @var
		28	## @item axdata
		29	## @var{n} by 2 matrix of data [@var{x}, @var{y}].
		30	## @end table
27	##	31	##
28	## @strong{Outputs}	32	## @strong{Output}
29	## @var{axvec} vector of axis limits appropriate for call to axis() function	33	## @table @var
		34	## @item axvec
		35	## Vector of axis limits appropriate for call to @command{axis} function.
		36	## @end table
30	## @end deftypefn	37	## @end deftypefn
31		38
32	function axvec = axis2dlim (axdata)	39	function axvec = axis2dlim (axdata)




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} prompt (@var{str})
## @format
## function prompt([str])
## Prompt user to continue
## 
## @strong{Input}
## @table @var
## @item str
## Input string. Its default value is: 
## @example 
## \n ---- Press a key to  continue ---
## @end example
## @end table
## @end deftypefn

## Author: David Clem




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{yy}, @var{idx}] =} sortcom (@var{xx}[, @var{opt}])
## Sort a complex vector.
## [yy,idx] = sortcom(xx[,opt]): sort a complex vector
## xx: complex vector
## opt: sorting option:
##  "re": real part (default)
##  "mag": by magnitude
##  "im": by imaginary part
##
## @strong{Inputs}
## @table @var
## @item xx
## Complex vector
## @item opt
## sorting option:
## @table @code
## @item "re"
## Real part (default);
## @item "mag"
## By magnitude;
## @item "im"
## By imaginary part.
## @end table
## if @var{opt} is not chosen as @code{"im"}, then complex conjugate pairs are grouped together,
## @math{a - jb} followed by @math{a + jb}.
## @end table
##
## @strong{Outputs}
## @table @var
## @item yy
## Sorted values
## @item idx
## Permutation vector: @code{yy = xx(idx)}
## @end table
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 17-25 Link Here

(-)octave-2.1.58/scripts/control/util/zgfmul.m (-3 / +3 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} zgfmul (@var{a}, @var{b}, @var{c}, @var{d}, @var{x})	20	## @deftypefn {Function File} {@var{y} =} zgfmul (@var{a}, @var{b}, @var{c}, @var{d}, @var{x})
21	## Compute product of zgep incidence matrix @math{F} with vector @var{x}.	21	## Compute product of @var{zgep} incidence matrix @math{F} with vector @var{x}.
22	## Used by zgepbal (in zgscal) as part of generalized conjugate gradient	22	## Used by @command{zgepbal} (in @command{zgscal}) as part of generalized conjugate gradient
23	## iteration.	23	## iteration.
24	## @end deftypefn	24	## @end deftypefn
25		25

Lines 17-26 Link Here

(-)octave-2.1.58/scripts/control/util/zginit.m (-3 / +3 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} zginit (@var{a}, @var{b}, @var{c}, @var{d})	20	## @deftypefn {Function File} {@var{zz} =} zginit (@var{a}, @var{b}, @var{c}, @var{d})
21	## Construct right hand side vector zz	21	## Construct right hand side vector @var{zz}
22	## for the zero-computation generalized eigenvalue problem	22	## for the zero-computation generalized eigenvalue problem
23	## balancing procedure. Called by zgepbal.	23	## balancing procedure. Called by @command{zgepbal}.
24	## @end deftypefn	24	## @end deftypefn
25		25
26	## References:	26	## References:




## -*- texinfo -*-
## @deftypefn {Function File} {} __zgpbal__ (@var{sys})
##
## Used internally in @command{tzero}; minimal argument checking performed.
##
## Implementation of zero computation generalized eigenvalue problem
## balancing method (Hodel and Tiller, Allerton Conference, 1991)
## Based on Ward's balancing algorithm (@acronym{SIAM} J. Sci Stat. Comput., 1981).
##
## @command{__zgpbal__} computes a state/input/output weighting that attempts to
## reduced the range of the magnitudes of the nonzero elements of [@var{a}, @var{b},
## @var{c}, @var{d}].
## The weighting uses scalar multiplication by powers of 2, so no roundoff
## will occur.
##
## @command{__zgpbal__} should be followed by @command{zgpred}.
## @end deftypefn

## References:

Lines 17-27 Link Here

(-)octave-2.1.58/scripts/control/util/zgscal.m (-3 / +2 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} zgscal (@var{f}, @var{z}, @var{n}, @var{m}, @var{p})	20	## @deftypefn {Function File} {@var{x} =} zgscal (@var{f}, @var{z}, @var{n}, @var{m}, @var{p})
21	## Generalized conjugate gradient iteration to	21	## Generalized conjugate gradient iteration to
22	## solve zero-computation generalized eigenvalue problem balancing equation	22	## solve zero-computation generalized eigenvalue problem balancing equation
23	## @math{fx=z};	23	## @math{fx=z}; called by @command{zgepbal}.
24	## called by @code{zgepbal}
25	## @end deftypefn	24	## @end deftypefn
26		25
27	## References:	26	## References:




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {@var{x} =} zgshsr (@var{y})
## Apply householder vector based on 
## @iftex
## @tex
## $ e^m $
## @end tex
## @end iftex
## @ifinfo
## @math{e^(m)}
## @end ifinfo
## to column vector @var{y}.
## Called by @command{zgfslv}.
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 18-24 Link Here

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18	## 02111-1307, USA.	18	## 02111-1307, USA.
19		19
20	## -- texinfo --	20	## -- texinfo --
21	## @deftypefn {Mapping Function} acoth (@var{x})	21	## @deftypefn {Mapping Function} {} acoth (@var{x})
22	## Compute the inverse hyperbolic cotangent of each element of @var{x}.	22	## Compute the inverse hyperbolic cotangent of each element of @var{x}.
23	## @end deftypefn	23	## @end deftypefn
24		24

Lines 40-46 Link Here

(-)octave-2.1.58/scripts/linear-algebra/commutation_matrix.m (-1 / +1 lines)
40	## matrix such that	40	## matrix such that
41	## @iftex	41	## @iftex
42	## @tex	42	## @tex
43	## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^T)$	43	## $K_{m,n} \cdot {\rm vec} (A) = {\rm vec} (A^{\rm T})$
44	## @end tex	44	## @end tex
45	## @end iftex	45	## @end iftex
46	## @ifinfo	46	## @ifinfo




## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} polyout (@var{c}, @var{x})
## Write formatted polynomial
## @iftex
## @tex
## $$ c(x) = c_1 x^n + \ldots + c_n x + c_{n+1} $$
## @end tex
## @end iftex
## @ifinfo
## @example
##    c(x) = c(1) * x^n + ... + c(n) x + c(n+1)
## @end example
## @end ifinfo
##  and return it as a string or write it to the screen (if
##  @var{nargout} is zero).
##  @var{x} defaults to the string @code{"s"}.
## @end deftypefn
## @seealso{polyval, polyvalm, poly, roots, conv, deconv, residue,
## filter, polyderiv, and polyinteg}

Lines 32-38 Link Here

(-)octave-2.1.58/scripts/polynomial/roots.m (-1 / +1 lines)
32	## @ifinfo	32	## @ifinfo
33	##	33	##
34	## @example	34	## @example
35	## v(1) * z^(N-1) + ... + v(N-1) * z + v(N).	35	## v(1) * z^(N-1) + ... + v(N-1) * z + v(N)
36	## @end example	36	## @end example
37	## @end ifinfo	37	## @end ifinfo
38	## @end deftypefn	38	## @end deftypefn

Lines 19-25 Link Here

(-)octave-2.1.58/scripts/specfun/log2.m (-1 / +1 lines)
19		19
20	## -- texinfo --	20	## -- texinfo --
21	## @deftypefn {Mapping Function} {} log2 (@var{x})	21	## @deftypefn {Mapping Function} {} log2 (@var{x})
22	## @deftypefnx {Mapping Function} {[@var{f}, @var{e}]} log2 (@var{x})	22	## @deftypefnx {Mapping Function} {[@var{f}, @var{e}] =} log2 (@var{x})
23	## Compute the base-2 logarithm of @var{x}. With two outputs, returns	23	## Compute the base-2 logarithm of @var{x}. With two outputs, returns
24	## @var{f} and @var{e} such that	24	## @var{f} and @var{e} such that
25	## @iftex	25	## @iftex

Lines 25-39 Link Here

(-)octave-2.1.58/scripts/special-matrix/toeplitz.m (-12 / +11 lines)
25	## @var{c} is used. If the second argument is omitted, the first row is	25	## @var{c} is used. If the second argument is omitted, the first row is
26	## taken to be the same as the first column.	26	## taken to be the same as the first column.
27	##	27	##
28	## A square Toeplitz matrix has the form	28	## A square Toeplitz matrix has the form:
29	## @iftex	29	## @iftex
30	## @tex	30	## @tex
31	## $$	31	## $$
32	## \left[\matrix{c_0 & r_1 & r_2 & \ldots & r_n\cr	32	## \left[\matrix{c_0 & r_1 & r_2 & \cdots & r_n\cr
33	## c_1 & c_0 & r_1 & & c_{n-1}\cr	33	## c_1 & c_0 & r_1 & \cdots & r_{n-1}\cr
34	## c_2 & c_1 & c_0 & & c_{n-2}\cr	34	## c_2 & c_1 & c_0 & \cdots & r_{n-2}\cr
35	## \vdots & & & & \vdots\cr	35	## \vdots & \vdots & \vdots & \ddots & \vdots\cr
36	## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right].	36	## c_n & c_{n-1} & c_{n-2} & \ldots & c_0}\right]
37	## $$	37	## $$
38	## @end tex	38	## @end tex
39	## @end iftex	39	## @end iftex
Lines 42-53 Link Here
42	## @example	42	## @example
43	## @group	43	## @group
44	## c(0) r(1) r(2) ... r(n)	44	## c(0) r(1) r(2) ... r(n)
45	## c(1) c(0) r(1) r(n-1)	45	## c(1) c(0) r(1) ... r(n-1)
46	## c(2) c(1) c(0) r(n-2)	46	## c(2) c(1) c(0) ... r(n-2)
47	## . .	47	## . , , . .
48	## . .	48	## . , , . .
49	## . .	49	## . , , . .
50	##
51	## c(n) c(n-1) c(n-2) ... c(0)	50	## c(n) c(n-1) c(n-2) ... c(0)
52	## @end group	51	## @end group
53	## @end example	52	## @end example

Lines 21-34 Link Here

(-)octave-2.1.58/scripts/special-matrix/vander.m (-12 / +11 lines)
21	## @deftypefn {Function File} {} vander (@var{c})	21	## @deftypefn {Function File} {} vander (@var{c})
22	## Return the Vandermonde matrix whose next to last column is @var{c}.	22	## Return the Vandermonde matrix whose next to last column is @var{c}.
23	##	23	##
24	## A Vandermonde matrix has the form	24	## A Vandermonde matrix has the form:
25	## @iftex	25	## @iftex
26	## @tex	26	## @tex
27	## $$	27	## $$
28	## \left[\matrix{c_0^n & \ldots & c_0^2 & c_0 & 1\cr	28	## \left[\matrix{c_1^{n-1} & \cdots & c_1^2 & c_1 & 1 \cr
29	## c_1^n & \ldots & c_1^2 & c_1 & 1\cr	29	## c_2^{n-1} & \cdots & c_2^2 & c_2 & 1 \cr
30	## \vdots & & \vdots & \vdots & \vdots\cr	30	## \vdots & \ddots & \vdots & \vdots & \vdots \cr
31	## c_n^n & \ldots & c_n^2 & c_n & 1}\right].	31	## c_n^{n-1} & \cdots & c_n^2 & c_n & 1 }\right]
32	## $$	32	## $$
33	## @end tex	33	## @end tex
34	## @end iftex	34	## @end iftex
Lines 36-48 Link Here
36	##	36	##
37	## @example	37	## @example
38	## @group	38	## @group
39	## c(0)^n ... c(0)^2 c(0) 1	39	## c(1)^(n-1) ... c(1)^2 c(1) 1
40	## c(1)^n ... c(1)^2 c(1) 1	40	## c(2)^(n-1) ... c(2)^2 c(2) 1
41	## . . . .	41	## . . . . .
42	## . . . .	42	## . . . . .
43	## . . . .	43	## . . . . .
44	##	44	## c(n)^(n-1) ... c(n)^2 c(n) 1
45	## c(n)^n ... c(n)^2 c(n) 1
46	## @end group	45	## @end group
47	## @end example	46	## @end example
48	## @end ifinfo	47	## @end ifinfo

Lines 601-607 tolerance must also be a vector of the s Link Here

(-)octave-2.1.58/src/DASPK-opts.cc (-1 / +2 lines)
601	The local error test applied at each integration step is\n\	601	The local error test applied at each integration step is\n\
602	\n\	602	\n\
603	@example\n\	603	@example\n\
604	abs (local error in x(i)) <= rtol(i) * abs (Y(i)) + atol(i)\n\	604	abs (local error in x(i)) <=\n\
		605	rtol(i) * abs (Y(i)) + atol(i)\n\
605	@end example\n\	606	@end example\n\
606	@item \"compute consistent initial condition\"\n\	607	@item \"compute consistent initial condition\"\n\
607	Denoting the differential variables in the state vector by @samp{Y_d}\n\	608	Denoting the differential variables in the state vector by @samp{Y_d}\n\

Lines 318-324 tolerance must also be a vector of the s Link Here

(-)octave-2.1.58/src/DASRT-opts.cc (-1 / +2 lines)
318	\n\	318	\n\
319	The local error test applied at each integration step is\n\	319	The local error test applied at each integration step is\n\
320	@example\n\	320	@example\n\
321	abs (local error in x(i)) <= rtol(i) * abs (Y(i)) + atol(i)\n\	321	abs (local error in x(i)) <=\n\
		322	rtol(i) * abs (Y(i)) + atol(i)\n\
322	@end example\n\	323	@end example\n\
323	@item \"initial step size\"\n\	324	@item \"initial step size\"\n\
324	Differential-algebraic problems may occaisionally suffer from severe\n\	325	Differential-algebraic problems may occaisionally suffer from severe\n\




  "-*- texinfo -*-\n\
@deftypefn {Loadable Function} {@var{lambda} =} qz (@var{a}, @var{b})\n\
Generalized eigenvalue problem @math{A x = s B x},\n\
@var{QZ} decomposition. There are three ways to call this function:\n\
@enumerate\n\
@item @code{lambda = qz(A,B)}\n\
\n\
Computes the generalized eigenvalues\n\
@iftex\n\
@tex\n\
$\\lambda$\n\
@end tex\n\
@end iftex\n\
@ifinfo\n\
@var{lambda}\n\
@end ifinfo\n\
of @math{(A - s B)}.\n\
@item @code{[AA, BB, Q, Z, V, W, lambda] = qz (A, B)}\n\
\n\
Computes qz decomposition, generalized eigenvectors, and \n\
        generalized eigenvalues of @math{(A - sB)}\n\
@iftex\n\
@tex\n\
$$ A\\,V = B\\,V\\,{ \\rm diag }(\\lambda) $$\n\
$$ W^{ \\rm T } A = { \\rm diag }(\\lambda)\\,W^{ \\rm T } B $$\n\
$$ AA = Q^{ \\rm T } A\\,Z,~ BB = Q^{ \\rm T } B\\,Z $$\n\
@end tex\n\
@end iftex\n\
@ifinfo\n\
@example\n\
@group\n\
        A*V = B*V*diag(lambda)\n\
        W'*A = diag(lambda)*W'*B\n\
        AA = Q'*A*Z, BB = Q'*B*Z\n\
@end group\n\
@end example\n\
@end ifinfo\n\
with @var{Q} and @var{Z} orthogonal (unitary)= @var{I}\n\
\n\
@item @code{[AA,BB,Z@{, lambda@}] = qz(A,B,opt)}\n\
\n\
As in form [2], but allows ordering of generalized eigenpairs\n\
        for (e.g.) solution of discrete time algebraic Riccati equations.\n\
        Form 3 is not available for complex matrices, and does not compute\n\
        the generalized eigenvectors @var{V}, @var{W}, nor the orthogonal matrix @var{Q}.\n\
@table @var\n\
@item opt\n\
 for ordering eigenvalues of the GEP pencil.  The leading  block\n\

Lines 228-234 output without change. For example,\n\ Link Here

(-)octave-2.1.58/src/DLD-FUNCTIONS/time.cc (-1 / +1 lines)
228	\n\	228	\n\
229	@example\n\	229	@example\n\
230	@group\n\	230	@group\n\
231	strftime (\"%r (%Z) %A %e %B %Y\", localtime (time ())\n\	231	strftime (\"%r (%Z) %A %e %B %Y\", localtime (time ()) )\n\
232	@result{} \"01:15:06 AM (CST) Monday 17 February 1997\"\n\	232	@result{} \"01:15:06 AM (CST) Monday 17 February 1997\"\n\
233	@end group\n\	233	@end group\n\
234	@end example\n\	234	@end example\n\

Lines 669-675 DEFUN (lasterr, args, , Link Here

(-)octave-2.1.58/src/error.cc (-2 / +2 lines)
669	@deftypefn {Built-in Function} {} lasterr ()\n\	669	@deftypefn {Built-in Function} {} lasterr ()\n\
670	@deftypefnx {Built-in Function} {} lasterr (@var{msg})\n\	670	@deftypefnx {Built-in Function} {} lasterr (@var{msg})\n\
671	Without any arguments, return the last error message. With one\n\	671	Without any arguments, return the last error message. With one\n\
672	argument, set the last warning message to @var{msg}.\n\	672	argument, set the last error message to @var{msg}.\n\
673	@end deftypefn")	673	@end deftypefn")
674	{	674	{
675	octave_value_list retval;	675	octave_value_list retval;
Lines 697-703 DEFUN (lastwarn, args, , Link Here
697	@deftypefn {Built-in Function} {} lastwarn ()\n\	697	@deftypefn {Built-in Function} {} lastwarn ()\n\
698	@deftypefnx {Built-in Function} {} lastwarn (@var{msg})\n\	698	@deftypefnx {Built-in Function} {} lastwarn (@var{msg})\n\
699	Without any arguments, return the last warning message. With one\n\	699	Without any arguments, return the last warning message. With one\n\
700	argument, set the last error message to @var{msg}.\n\	700	argument, set the last warning message to @var{msg}.\n\
701	@end deftypefn")	701	@end deftypefn")
702	{	702	{
703	octave_value_list retval;	703	octave_value_list retval;

Lines 1751-1757 DEFUN (mkstemp, args, , Link Here

(-)octave-2.1.58/src/file-io.cc (-1 / +1 lines)
1751	@deftypefn {Built-in Function} {[@var{fid}, @var{name}, @var{msg}] =} tmpfile (@var{template}, @var{delete})\n\	1751	@deftypefn {Built-in Function} {[@var{fid}, @var{name}, @var{msg}] =} tmpfile (@var{template}, @var{delete})\n\
1752	Return the file ID corresponding to a new temporary file with a unique\n\	1752	Return the file ID corresponding to a new temporary file with a unique\n\
1753	name created from @var{template}. The last six characters of @var{template}\n\	1753	name created from @var{template}. The last six characters of @var{template}\n\
1754	must be @code{XXXXXX} and tehse are replaced with a string that makes the\n\	1754	must be @code{XXXXXX} and these are replaced with a string that makes the\n\
1755	filename unique. The file is then created with mode read/write and\n\	1755	filename unique. The file is then created with mode read/write and\n\
1756	permissions that are system dependent (on GNU/Linux systems, the permissions\n\	1756	permissions that are system dependent (on GNU/Linux systems, the permissions\n\
1757	will be 0600 for versions of glibc 2.0.7 and later). The file is opened\n\	1757	will be 0600 for versions of glibc 2.0.7 and later). The file is opened\n\

Lines 1128-1137 value of @code{PS2} is @code{\"> \"}.\n\ Link Here

(-)octave-2.1.58/src/input.cc (-2 / +2 lines)
1128	DEFVAR (PS4, "+ ", ps4,	1128	DEFVAR (PS4, "+ ", ps4,
1129	"-- texinfo --\n\	1129	"-- texinfo --\n\
1130	@defvr {Built-in Variable} PS4\n\	1130	@defvr {Built-in Variable} PS4\n\
1131	If Octave is invoked with the @code{--echo-input} option, the value of\n\	1131	If Octave is invoked with the @code{--echo-commands} option, the value of\n\
1132	@code{PS4} is printed before each line of input that is echoed. The\n\	1132	@code{PS4} is printed before each line of input that is echoed. The\n\
1133	default value of @code{PS4} is @code{\"+ \"}. @xref{Invoking Octave}, for\n\	1133	default value of @code{PS4} is @code{\"+ \"}. @xref{Invoking Octave}, for\n\
1134	a description of @code{--echo-input}.\n\	1134	a description of @code{--echo-commands}.\n\
1135	@end defvr");	1135	@end defvr");
1136		1136
1137	DEFVAR (completion_append_char, " ", completion_append_char,	1137	DEFVAR (completion_append_char, " ", completion_append_char,




@ifinfo\n\
@var{theta} = @code{atan (@var{y}/@var{x})}.\n\
@end ifinfo\n\
\n\
@noindent\n\
in radians. \n\
\n\

  DEFUN_MAPPER (asinh, 0, 0, 0, asinh, 0, asinh, 0.0, 0.0, 0, 0,
    "-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} asinh (@var{x})\n\
Compute the inverse hyperbolic sine of each element of @var{x}.\n\
@end deftypefn");

  DEFUN_MAPPER (atan, 0, 0, 0, atan, 0, atan, 0.0, 0.0, 0, 0,

  DEFUN_MAPPER (atanh, 0, 0, 0, atanh, 0, atanh, -1.0, 1.0, 0, 1,
    "-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} atanh (@var{x})\n\
Compute the inverse hyperbolic tangent of each element of @var{x}.\n\
@end deftypefn");

  DEFUN_MAPPER (ceil, 0, 0, 0, ceil, 0, ceil, 0.0, 0.0, 0, 0,

\n\
@example\n\
@group\n\
finite ([13, Inf, NA, NaN])\n\
     @result{} [ 1, 0, 0, 0 ]\n\
@end group\n\
@end example\n\
@end deftypefn");

  DEFUN_MAPPER (sin, 0, 0, 0, sin, 0, sin, 0.0, 0.0, 0, 0,
    "-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} sin (@var{x})\n\
Compute the sine of each element of @var{x}.\n\
@end deftypefn");

  DEFUN_MAPPER (sinh, 0, 0, 0, sinh, 0, sinh, 0.0, 0.0, 0, 0,
    "-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} sinh (@var{x})\n\
Compute the inverse hyperbolic sine of each element of @var{x}.\n\
@end deftypefn");

  DEFUN_MAPPER (sqrt, 0, 0, 0, sqrt, 0, sqrt, 0.0, octave_Inf, 0, 1,

  DEFUN_MAPPER (tan, 0, 0, 0, tan, 0, tan, 0.0, 0.0, 0, 0,
    "-*- texinfo -*-\n\
@deftypefn {Mapping Function} {} tan (@var{z})\n\
Compute tangent of each element of @var{x}.\n\
@end deftypefn");

  DEFUN_MAPPER (tanh, 0, 0, 0, tanh, 0, tanh, 0.0, 0.0, 0, 0,

Lines 358-364 parameter may only be a scalar.\n\ Link Here

(-)octave-2.1.58/src/ODESSA-opts.cc (-1 / +2 lines)
358	The local error test applied at each integration step is\n\	358	The local error test applied at each integration step is\n\
359	\n\	359	\n\
360	@example\n\	360	@example\n\
361	abs (local error in x(i)) <= rtol * abs (y(i)) + atol(i)\n\	361	abs (local error in x(i)) <=\n\
		362	rtol * abs (y(i)) + atol(i)\n\
362	@end example\n\	363	@end example\n\
363	@item \"integration method\"\n\	364	@item \"integration method\"\n\
364	A string specifing the method of integration to use to solve the ODE\n\	365	A string specifing the method of integration to use to solve the ODE\n\

Lines 334-340 symbols_of_pt_assign (void) Link Here

(-)octave-2.1.58/src/pt-assign.cc (-1 / +1 lines)
334	{	334	{
335	DEFVAR (print_rhs_assign_val, false, print_rhs_assign_val,	335	DEFVAR (print_rhs_assign_val, false, print_rhs_assign_val,
336	"-- texinfo --\n\	336	"-- texinfo --\n\
337	@defvr print_rhs_assign_val\n\	337	@defvr {Built-in Variable} print_rhs_assign_val\n\
338	If the value of this variable is non-zero, Octave will print the value\n\	338	If the value of this variable is non-zero, Octave will print the value\n\
339	of the right hand side of assignment expressions instead of the value\n\	339	of the right hand side of assignment expressions instead of the value\n\
340	of the left hand side (after the assignment).\n\	340	of the left hand side (after the assignment).\n\

Lines 1358-1364 is @code{\"gnuplot\"}. @xref{Installati Link Here

(-)octave-2.1.58/src/pt-plot.cc (-1 / +1 lines)
1358	@defvr {Built-in Variable} gnuplot_has_frames\n\	1358	@defvr {Built-in Variable} gnuplot_has_frames\n\
1359	If the value of this variable is nonzero, Octave assumes that your copy\n\	1359	If the value of this variable is nonzero, Octave assumes that your copy\n\
1360	of gnuplot has support for multiple frames that is included in recent\n\	1360	of gnuplot has support for multiple frames that is included in recent\n\
1361	3.6beta releases. It's initial value is determined by configure, but it\n\	1361	3.6beta releases. Its initial value is determined by configure, but it\n\
1362	can be changed in your startup script or at the command line in case\n\	1362	can be changed in your startup script or at the command line in case\n\
1363	configure got it wrong, or if you upgrade your gnuplot installation.\n\	1363	configure got it wrong, or if you upgrade your gnuplot installation.\n\
1364	@end defvr");	1364	@end defvr");

Lines 1741-1747 symbols_of_symtab (void) Link Here

(-)octave-2.1.58/src/symtab.cc (-1 / +1 lines)
1741	{	1741	{
1742	DEFVAR (variables_can_hide_functions, true, variables_can_hide_functions,	1742	DEFVAR (variables_can_hide_functions, true, variables_can_hide_functions,
1743	"-- texinfo --\n\	1743	"-- texinfo --\n\
1744	@defvr variables_can_hide_functions\n\	1744	@defvr {Built-in Variable} variables_can_hide_functions\n\
1745	If the value of this variable is nonzero, assignments to variables may\n\	1745	If the value of this variable is nonzero, assignments to variables may\n\
1746	hide previously defined functions of the same name. A negative value\n\	1746	hide previously defined functions of the same name. A negative value\n\
1747	will cause Octave to print a warning, but allow the operation.\n\	1747	will cause Octave to print a warning, but allow the operation.\n\

Return to bug 62982

Lines 108-137 $\pi/180$ Link Here

(-)octave-2.1.58/doc/interpreter/arith.txi (-4 / +4 lines)
108	@DOCSTRING(sin)	108	@DOCSTRING(sin)
109	@DOCSTRING(cos)	109	@DOCSTRING(cos)
110	@DOCSTRING(tan)	110	@DOCSTRING(tan)
		111	@DOCSTRING(cot)
111	@DOCSTRING(sec)	112	@DOCSTRING(sec)
112	@DOCSTRING(csc)	113	@DOCSTRING(csc)
113	@DOCSTRING(cot)
114		114
115	@DOCSTRING(asin)	115	@DOCSTRING(asin)
116	@DOCSTRING(acos)	116	@DOCSTRING(acos)
117	@DOCSTRING(atan)	117	@DOCSTRING(atan)
		118	@DOCSTRING(acot)
118	@DOCSTRING(asec)	119	@DOCSTRING(asec)
119	@DOCSTRING(acsc)	120	@DOCSTRING(acsc)
120	@DOCSTRING(acot)
121		121
122	@DOCSTRING(sinh)	122	@DOCSTRING(sinh)
123	@DOCSTRING(cosh)	123	@DOCSTRING(cosh)
124	@DOCSTRING(tanh)	124	@DOCSTRING(tanh)
		125	@DOCSTRING(coth)
125	@DOCSTRING(sech)	126	@DOCSTRING(sech)
126	@DOCSTRING(csch)	127	@DOCSTRING(csch)
127	@DOCSTRING(coth)
128		128
129	@DOCSTRING(asinh)	129	@DOCSTRING(asinh)
130	@DOCSTRING(acosh)	130	@DOCSTRING(acosh)
131	@DOCSTRING(atanh)	131	@DOCSTRING(atanh)
		132	@DOCSTRING(acoth)
132	@DOCSTRING(asech)	133	@DOCSTRING(asech)
133	@DOCSTRING(acsch)	134	@DOCSTRING(acsch)
134	@DOCSTRING(acoth)
135		135
136	Each of these functions expect a single argument. For matrix arguments,	136	Each of these functions expect a single argument. For matrix arguments,
137	they work on an element by element basis. For example,	137	they work on an element by element basis. For example,

Lines 5-11 Link Here

(-)octave-2.1.58/doc/interpreter/control.txi (-13 / +13 lines)
5	@node Control Theory	5	@node Control Theory
6	@chapter Control Theory	6	@chapter Control Theory
7		7
8	The Octave Control Systems Toolbox (OCST) was initially developed	8	The Octave Control Systems Toolbox (@acronym{OCST}) was initially developed
9	by Dr.@: A. Scottedward Hodel	9	by Dr.@: A. Scottedward Hodel
10	@email{a.s.hodel@@eng.auburn.edu} with the assistance	10	@email{a.s.hodel@@eng.auburn.edu} with the assistance
11	of his students	11	of his students
Lines 15-27 of his students Link Here
15	@item John E. Ingram @email{John.Ingram@@sea.siemans.com}, and	15	@item John E. Ingram @email{John.Ingram@@sea.siemans.com}, and
16	@item Kristi McGowan.	16	@item Kristi McGowan.
17	@end itemize	17	@end itemize
18	This development was supported in part by NASA's Marshall Space Flight	18	This development was supported in part by @acronym{NASA}'s Marshall Space Flight
19	Center as part of an in-house CACSD environment. Additional important	19	Center as part of an in-house @acronym{CACSD} environment. Additional important
20	contributions were made by Dr. Kai Mueller @email{mueller@@ifr.ing.tu-bs.de}	20	contributions were made by Dr. Kai Mueller @email{mueller@@ifr.ing.tu-bs.de}
21	and Jose Daniel Munoz Frias (@code{place.m}).	21	and Jose Daniel Munoz Frias (@code{place.m}).
22		22
23	An on-line menu-driven tutorial is available via @code{DEMOcontrol};	23	An on-line menu-driven tutorial is available via @code{DEMOcontrol};
24	beginning OCST users should start with this program.	24	beginning @acronym{OCST} users should start with this program.
25		25
26	@DOCSTRING(DEMOcontrol)	26	@DOCSTRING(DEMOcontrol)
27		27
Lines 48-74 beginning OCST users should start with t Link Here
48	* sysstructss::	48	* sysstructss::
49	@end menu	49	@end menu
50		50
51	The OCST stores all dynamic systems in	51	The @acronym{OCST} stores all dynamic systems in
52	a single data structure format that can represent continuous systems,	52	a single data structure format that can represent continuous systems,
53	discrete-systems, and mixed (hybrid) systems in state-space form, and	53	discrete-systems, and mixed (hybrid) systems in state-space form, and
54	can also represent purely continuous/discrete systems in either	54	can also represent purely continuous/discrete systems in either
55	transfer function or pole-zero form. In order to	55	transfer function or pole-zero form. In order to
56	provide more flexibility in treatment of discrete/hybrid systems, the	56	provide more flexibility in treatment of discrete/hybrid systems, the
57	OCST also keeps a record of which system outputs are sampled.	57	@acronym{OCST} also keeps a record of which system outputs are sampled.
58		58
59	Octave structures are accessed with a syntax much like that used	59	Octave structures are accessed with a syntax much like that used
60	by the C programming language. For consistency in	60	by the C programming language. For consistency in
61	use of the data structure used in the OCST, it is recommended that	61	use of the data structure used in the @acronym{OCST}, it is recommended that
62	the system structure access m-files be used (@pxref{sysinterface}).	62	the system structure access m-files be used (@pxref{sysinterface}).
63	Some elements of the data structure are absent depending on the internal	63	Some elements of the data structure are absent depending on the internal
64	system representation(s) used. More than one system representation	64	system representation(s) used. More than one system representation
65	can be used for SISO systems; the OCST m-files ensure that all representations	65	can be used for @acronym{SISO} systems; the @acronym{OCST} m-files ensure that all representations
66	used are consistent with one another.	66	used are consistent with one another.
67		67
68	@DOCSTRING(sysrepdemo)	68	@DOCSTRING(sysrepdemo)
69		69
70	@node sysstructvars	70	@node sysstructvars
71	@subsection Variables common to all OCST system formats	71	@subsection Variables common to all @acronym{OCST} system formats
72		72
73	The data structure elements (and variable types) common to all system	73	The data structure elements (and variable types) common to all system
74	representations are listed below; examples of the initialization	74	representations are listed below; examples of the initialization
Lines 176-182 names of system states (list of string Link Here
176	@node sysinterface	176	@node sysinterface
177	@section System Construction and Interface Functions	177	@section System Construction and Interface Functions
178		178
179	Construction and manipulations of the OCST system data structure	179	Construction and manipulations of the @acronym{OCST} system data structure
180	(@pxref{sysstruct}) requires attention to many details in order	180	(@pxref{sysstruct}) requires attention to many details in order
181	to ensure that data structure contents remain consistent. Users	181	to ensure that data structure contents remain consistent. Users
182	are strongly encouraged to use the system interface functions	182	are strongly encouraged to use the system interface functions
Lines 352-364 system data structures. Link Here
352		352
353	@DOCSTRING(zgshsr)	353	@DOCSTRING(zgshsr)
354		354
355	References:	355	@strong{References}
356	@table @strong	356	@table @strong
357	@item ZGEP	357	@item ZGEP
358	Hodel, "Computation of Zeros with Balancing," 1992, Linear Algebra	358	Hodel, @cite{Computation of Zeros with Balancing}, 1992, Linear Algebra
359	and its Applications	359	and its Applications
360	@item @strong{Generalized CG}	360	@item @strong{Generalized CG}
361	Golub and Van Loan, "Matrix Computations, 2nd ed" 1989	361	Golub and Van Loan, @cite{Matrix Computations, 2nd ed} 1989.
362	@end table	362	@end table
363		363
364	@node sysprop	364	@node sysprop

Lines 67-141 a (1, :) Link Here

(-)octave-2.1.58/doc/interpreter/expr.txi (-69 / +3 lines)
67	@noindent	67	@noindent
68	and select the first row of the matrix.	68	and select the first row of the matrix.
69		69
70	A special form of indexing may be used to select elements of a matrix or	70	@c FIXED -- sections on variable prefer_zero_one_indexing were removed
71	vector. If the indices are vectors made up of only ones and zeros, the
72	result is a new matrix whose elements correspond to the elements of the
73	index vector that are equal to one. For example,
74		71
75	@example	72	Indexing a scalar with a vector of ones can be used to create a
76	@group
77	a = [1, 2; 3, 4];
78	a ([1, 0], :)
79	@end group
80	@end example
81
82	@noindent
83	selects the first row of the matrix @code{a}.
84
85	This operation can be useful for selecting elements of a matrix based on
86	some condition, since the comparison operators return matrices of ones
87	and zeros.
88
89	This special zero-one form of indexing leads to a conflict with the
90	standard indexing operation. For example, should the following
91	statements
92
93	@example
94	@group
95	a = [1, 2; 3, 4];
96	a ([1, 1], :)
97	@end group
98	@end example
99
100	@noindent
101	return the original matrix, or the matrix formed by selecting the first
102	row twice? Although this conflict is not likely to arise very often in
103	practice, you may select the behavior you prefer by setting the built-in
104	variable @code{prefer_zero_one_indexing}.
105
106	@c XXX FIXME XXX -- this variable no longer exists!
107
108	@defvr {Built-in Variable} prefer_zero_one_indexing
109	If the value of @code{prefer_zero_one_indexing} is nonzero, Octave
110	will perform zero-one style indexing when there is a conflict with the
111	normal indexing rules. @xref{Index Expressions}. For example, given a
112	matrix
113
114	@example
115	a = [1, 2, 3, 4]
116	@end example
117
118	@noindent
119	with @code{prefer_zero_one_indexing} is set to nonzero, the
120	expression
121
122	@example
123	a ([1, 1, 1, 1])
124	@end example
125
126	@noindent
127	results in the matrix @code{[ 1, 2, 3, 4 ]}. If the value of
128	@code{prefer_zero_one_indexing} set to 0, the result would be
129	the matrix @code{[ 1, 1, 1, 1 ]}.
130
131	In the first case, Octave is selecting each element corresponding to a
132	@samp{1} in the index vector. In the second, Octave is selecting the
133	first element multiple times.
134
135	The default value for @code{prefer_zero_one_indexing} is 0.
136	@end defvr
137
138	Finally, indexing a scalar with a vector of ones can be used to create a
139	vector the same size as the index vector, with each element equal to	73	vector the same size as the index vector, with each element equal to
140	the value of the original scalar. For example, the following statements	74	the value of the original scalar. For example, the following statements
141		75
Lines 890-896 A (:, 1:2:5) = [] Link Here
890	@end example	824	@end example
891		825
892	@noindent	826	@noindent
893	deletes the first, third, and fifth columns.	827	deletes the first, second, and fifth columns.
894		828
895	An assignment is an expression, so it has a value. Thus, @code{z = 1}	829	An assignment is an expression, so it has a value. Thus, @code{z = 1}
896	as an expression has the value 1. One consequence of this is that you	830	as an expression has the value 1. One consequence of this is that you

Lines 375-381 does contain a nonzero element. Link Here

(-)octave-2.1.58/doc/interpreter/func.txi (-4 / +2 lines)
375		375
376	@defvr {Keyword} return	376	@defvr {Keyword} return
377	When Octave encounters the keyword @code{return} inside a function or	377	When Octave encounters the keyword @code{return} inside a function or
378	script, it returns control to be caller immediately. At the top level,	378	script, it returns control to the caller immediately. At the top level,
379	the return statement is ignored. A @code{return} statement is assumed	379	the return statement is ignored. A @code{return} statement is assumed
380	at the end of every function definition.	380	at the end of every function definition.
381	@end defvr	381	@end defvr
Lines 667-674 The next statements Link Here
667		667
668	@example	668	@example
669	@group	669	@group
670	ColumnVector dx (3);
671
672	dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)	670	dx(0) = 77.27 * (x(1) - x(0)*x(1) + x(0)
673	- 8.375e-06*pow (x(0), 2));	671	- 8.375e-06*pow (x(0), 2));
674		672
Lines 679-685 dx(2) = 0.161*(x(0) - x(2)); Link Here
679	@end example	677	@end example
680		678
681	@noindent	679	@noindent
682	define the right hand side of the differential equation. Finally, we	680	define the right-hand side of the differential equation. Finally, we
683	can return @code{dx}:	681	can return @code{dx}:
684		682
685	@example	683	@example

Lines 32-38 function analdemo () Link Here

(-)octave-2.1.58/scripts/control/base/analdemo.m (-12 / +12 lines)
32	k=0;	32	k=0;
33	while(k > 8 \|\| k < 1)	33	while(k > 8 \|\| k < 1)
34	k = menu("Octave State Space Analysis Demo", ...	34	k = menu("Octave State Space Analysis Demo", ...
35	"System grammians (gram, dgram)", ...	35	"System gramians (gram, dgram)", ...
36	"System zeros (tzero)", ...	36	"System zeros (tzero)", ...
37	"Continuous => Discrete and Discrete => Continuous conversions (c2d,d2c)", ...	37	"Continuous => Discrete and Discrete => Continuous conversions (c2d,d2c)", ...
38	"Algebraic Riccati Equation (are, dare)", ...	38	"Algebraic Riccati Equation (are, dare)", ...
Lines 47-68 function analdemo () Link Here
47	prompt	47	prompt
48		48
49	clc	49	clc
50	disp("System Grammians: (see Moore, IEEE T-AC, 1981) \n");	50	disp("System Gramians: (see Moore, IEEE T-AC, 1981) \n");
51	disp("Example #1, consider the discrete time state space system:\n");	51	disp("Example #1, consider the discrete time state space system:\n");
52	a=[1, 5, -8.4; 1.2, -3, 5; 1, 7, 9]	52	a=[1, 5, -8.4; 1.2, -3, 5; 1, 7, 9]
53	b=[1, 5; 2, 6; -4.4, 5]	53	b=[1, 5; 2, 6; -4.4, 5]
54	c=[1, -1.5, 2; 6, -9.8, 1]	54	c=[1, -1.5, 2; 6, -9.8, 1]
55	d=0	55	d=0
56	prompt	56	prompt
57	disp("\nThe discrete controllability grammian is computed as follows:");	57	disp("\nThe discrete controllability gramian is computed as follows:");
58	cmd = "grammian = dgram(a, b);";	58	cmd = "gramian = dgram(a, b);";
59	run_cmd;	59	run_cmd;
60	disp("Results:\n");	60	disp("Results:\n");
61	grammian = dgram(a,b)	61	gramian = dgram(a,b)
62	disp("Variable Description:\n");	62	disp("Variable Description:\n");
63	disp("grammian => discrete controllability grammian");	63	disp("gramian => discrete controllability gramian");
64	disp("a, b => a and b matrices of discrete time system\n");	64	disp("a, b => a and b matrices of discrete time system\n");
65	disp("A dual approach may be used to compute the observability grammian.");	65	disp("A dual approach may be used to compute the observability gramian.");
66	prompt	66	prompt
67	clc	67	clc
68		68
Lines 76-90 function analdemo () Link Here
76	c=[1, -1.1, 7; 3, -9.8, 2]	76	c=[1, -1.1, 7; 3, -9.8, 2]
77	d=0	77	d=0
78	prompt	78	prompt
79	disp("\nThe continuous controllability grammian is computed as follows:");	79	disp("\nThe continuous controllability gramian is computed as follows:");
80	cmd = "grammian = gram(a, b);";	80	cmd = "gramian = gram(a, b);";
81	run_cmd;	81	run_cmd;
82	disp("Results:\n");	82	disp("Results:\n");
83	grammian = gram(a,b)	83	gramian = gram(a,b)
84	disp("Variable Description:\n");	84	disp("Variable Description:\n");
85	disp("grammian => continuous controllability grammian");	85	disp("gramian => continuous controllability gramian");
86	disp("a, b => a and b matrices of continuous time system\n");	86	disp("a, b => a and b matrices of continuous time system\n");
87	disp("A dual approach may be used to compute the observability grammian.");	87	disp("A dual approach may be used to compute the observability gramian.");
88	prompt	88	prompt
89	clc	89	clc
90		90

Lines 17-28 Link Here

(-)octave-2.1.58/scripts/control/base/are.m (-11 / +14 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} are (@var{a}, @var{b}, @var{c}, @var{opt})	20	## @deftypefn {Function File} {@var{x} =} are (@var{a}, @var{b}, @var{c}, @var{opt})
21	## Solve the algebraic Riccati equation	21	## Solve the Algebraic Riccati Equation
22	## @iftex	22	## @iftex
23	## @tex	23	## @tex
24	## $$	24	## $$
25	## A^TX + XA - XBX + C = 0	25	## A^{ \rm T }\,X + X\,A - X\,B\,X + C = 0
26	## $$	26	## $$
27	## @end tex	27	## @end tex
28	## @end iftex	28	## @end iftex
Lines 37-59 Link Here
37	## for identically dimensioned square matrices	37	## for identically dimensioned square matrices
38	## @table @var	38	## @table @var
39	## @item a	39	## @item a
40	## @var{n}x@var{n} matrix.	40	## @var{n} by @var{n} matrix;
41	## @item b	41	## @item b
42	## @var{n}x@var{n} matrix or @var{n}x@var{m} matrix; in the latter case	42	## @var{n} by @var{n} matrix or @var{n} by @var{m} matrix; in the latter case
43	## @var{b} is replaced by @math{b:=b*b'}.	43	## @var{b} is replaced by @math{b:=b*b'};
44	## @item c	44	## @item c
45	## @var{n}x@var{n} matrix or @var{p}x@var{m} matrix; in the latter case	45	## @var{n} by @var{n} matrix or @var{p} by @var{m} matrix; in the latter case
46	## @var{c} is replaced by @math{c:=c'*c}.	46	## @var{c} is replaced by @math{c:=c'*c};
47	## @item opt	47	## @item opt
48	## (optional argument; default = @code{"B"}):	48	## (optional argument; default = @code{"B"}):
49	## String option passed to @code{balance} prior to ordered Schur decomposition.	49	## String option passed to @code{balance} prior to ordered Schur decomposition.
50	## @end table	50	## @end table
51	##	51	##
52	## @strong{Outputs}	52	## @strong{Output}
53	## @var{x}: solution of the ARE.	53	## @table @var
		54	## @item x
		55	## solution of the @acronym{ARE}.
		56	## @end table
54	##	57	##
55	## @strong{Method}	58	## @strong{Method}
56	## Laub's Schur method (IEEE Transactions on	59	## Laub's Schur method (@acronym{IEEE} Transactions on
57	## Automatic Control, 1979) is applied to the appropriate Hamiltonian	60	## Automatic Control, 1979) is applied to the appropriate Hamiltonian
58	## matrix.	61	## matrix.
59	##	62	##

Lines 20-28 Link Here

(-)octave-2.1.58/scripts/control/base/bode_bounds.m (-2 / +10 lines)
20	## @deftypefn {Function File} {[@var{wmin}, @var{wmax}] =} bode_bounds (@var{zer}, @var{pol}, @var{dflg}, @var{tsam})	20	## @deftypefn {Function File} {[@var{wmin}, @var{wmax}] =} bode_bounds (@var{zer}, @var{pol}, @var{dflg}, @var{tsam})
21	## Get default range of frequencies based on cutoff frequencies of system	21	## Get default range of frequencies based on cutoff frequencies of system
22	## poles and zeros.	22	## poles and zeros.
23	## Frequency range is the interval [10^wmin,10^wmax]	23	## Frequency range is the interval
		24	## @iftex
		25	## @tex
		26	## $ [ 10^{w_{min}},~10^{w_{max}} ] $
		27	## @end tex
		28	## @end iftex
		29	## @ifinfo
		30	## [10^@var{wmin}, 10^@var{wmax}]
		31	## @end ifinfo
24	##	32	##
25	## Used internally in __freqresp__ (@code{bode}, @code{nyquist})	33	## Used internally in @command{__freqresp__} (@command{bode}, @command{nyquist})
26	## @end deftypefn	34	## @end deftypefn
27		35
28	function [wmin, wmax] = bode_bounds (zer, pol, DIGITAL, tsam)	36	function [wmin, wmax] = bode_bounds (zer, pol, DIGITAL, tsam)

Lines 19-34 Link Here

(-)octave-2.1.58/scripts/control/base/ctrb.m (-3 / +10 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} ctrb (@var{sys}, @var{b})	20	## @deftypefn {Function File} {} ctrb (@var{sys}, @var{b})
21	## @deftypefnx {Function File} {} ctrb (@var{a}, @var{b})	21	## @deftypefnx {Function File} {} ctrb (@var{a}, @var{b})
22	## Build controllability matrix	22	## Build controllability matrix:
		23	## @iftex
		24	## @tex
		25	## $$ Q_s = [ ~ B ~ A\,B ~ A^2B ~ \ldots ~ A^{n-1}B ~ ] $$
		26	## @end tex
		27	## @end iftex
		28	## @ifinfo
23	## @example	29	## @example
24	## 2 n-1	30	## 2 n-1
25	## Qs = [ B AB A B ... A B ]	31	## Qs = [ B AB A B ... A B ]
26	## @end example	32	## @end example
		33	## @end ifinfo
27	##	34	##
28	## of a system data structure or the pair (@var{a}, @var{b}).	35	## of a system data structure or the pair (@var{a}, @var{b}).
29	##	36	##
30	## @code{ctrb} forms the controllability matrix.	37	## @command{ctrb} forms the controllability matrix.
31	## The numerical properties of @code{is_controllable}	38	## The numerical properties of @command{is_controllable}
32	## are much better for controllability tests.	39	## are much better for controllability tests.
33	## @end deftypefn	40	## @end deftypefn
34		41

Lines 19-25 Link Here

(-)octave-2.1.58/scripts/control/base/DEMOcontrol.m (-3 / +3 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} DEMOcontrol	20	## @deftypefn {Function File} {} DEMOcontrol
21	## Octave Control Systems Toolbox demo/tutorial program. The demo	21	## Octave Control Systems Toolbox demo/tutorial program. The demo
22	## allows the user to select among several categories of OCST function:	22	## allows the user to select among several categories of @acronym{OCST} function:
23	## @example	23	## @example
24	## @group	24	## @group
25	## octave:1> DEMOcontrol	25	## octave:1> DEMOcontrol
Lines 36-42 Link Here
36	## @end group	36	## @end group
37	## @end example	37	## @end example
38	## Command examples are interactively run for users to observe the use	38	## Command examples are interactively run for users to observe the use
39	## of OCST functions.	39	## of @acronym{OCST} functions.
40	## @end deftypefn	40	## @end deftypefn
41	## @seealso{Demo Programs: bddemo.m, frdemo.m, analdemo.m,	41	## @seealso{Demo Programs: bddemo.m, frdemo.m, analdemo.m,
42	## moddmeo.m, rldemo.m}	42	## moddmeo.m, rldemo.m}
Lines 46-52 Link Here
46		46
47	function DEMOcontrol ()	47	function DEMOcontrol ()
48		48
49	puts ("O C T A V E C O N T R O L S Y S T E M S T O O L B O X")	49	puts ("O C T A V E C O N T R O L S Y S T E M S T O O L B O X");
50		50
51	while (1)	51	while (1)
52		52

Lines 17-23 Link Here

(-)octave-2.1.58/scripts/control/base/dre.m (-15 / +21 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{tvals}, @var{plist}] =} dre (@var{sys}, @var{q}, @var{r}, @var{qf}, @var{t0}, @var{tf}, @var{ptol}, @var{maxits});	20	## @deftypefn {Function File} {[@var{tvals}, @var{plist}] =} dre (@var{sys}, @var{q}, @var{r}, @var{qf}, @var{t0}, @var{tf}, @var{ptol}, @var{maxits})
21	## Solve the differential Riccati equation	21	## Solve the differential Riccati equation
22	## @ifinfo	22	## @ifinfo
23	## @example	23	## @example
Lines 27-46 Link Here
27	## @end ifinfo	27	## @end ifinfo
28	## @iftex	28	## @iftex
29	## @tex	29	## @tex
30	## $$ -{dP \over dt} = A^T P+PA-PBR^{-1}B^T P+Q $$	30	## $$ -{dP \over dt} = A^{ \rm T } P+PA-PBR^{-1}B^{ \rm T } P+Q $$
31	## $$ P(t_f) = Qf $$	31	## $$ P(t_f) = Q_f $$
32	## @end tex	32	## @end tex
33	## @end iftex	33	## @end iftex
34	## for the LTI system sys. Solution of standard LTI	34	## for the @acronym{LTI} system sys. Solution of
35	## state feedback optimization	35	## standard @acronym{LTI} state feedback optimization
36	## @ifinfo	36	## @ifinfo
37	## @example	37	## @example
38	## min \int_@{t_0@}^@{t_f@} x' Q x + u' R u dt + x(t_f)' Qf x(t_f)	38	## min int(t0, tf) ( x' Q x + u' R u ) dt + x(tf)' Qf x(tf)
39	## @end example	39	## @end example
40	## @end ifinfo	40	## @end ifinfo
41	## @iftex	41	## @iftex
42	## @tex	42	## @tex
43	## $$ \min \int_{t_0}^{t_f} x^T Q x + u^T R u dt + x(t_f)^T Qf x(t_f) $$	43	## $$ \min \int_{t_0}^{t_f} x^{ \rm T } Q x + u^{ \rm T } R u dt + x(t_f)^{ \rm T } Q_f x(t_f) $$
44	## @end tex	44	## @end tex
45	## @end iftex	45	## @end iftex
46	## optimal input is	46	## optimal input is
Lines 51-57 Link Here
51	## @end ifinfo	51	## @end ifinfo
52	## @iftex	52	## @iftex
53	## @tex	53	## @tex
54	## $$ u = - R^{-1} B^T P(t) x $$	54	## $$ u = - R^{-1} B^{ \rm T } P(t) x $$
55	## @end tex	55	## @end tex
56	## @end iftex	56	## @end iftex
57	## @strong{Inputs}	57	## @strong{Inputs}
Lines 77-91 Link Here
77	## @item tvals	77	## @item tvals
78	## time values at which @var{p}(@var{t}) is computed	78	## time values at which @var{p}(@var{t}) is computed
79	## @item plist	79	## @item plist
80	## list values of @var{p}(@var{t}); @var{plist} @{ @var{ii} @}	80	## list values of @var{p}(@var{t}); @var{plist} @{ @var{i} @}
81	## is @var{p}(@var{tvals}(@var{ii})).	81	## is @var{p}(@var{tvals}(@var{i}))
82	##	82	## @end table
83	## @item tvals	83	## @var{tvals} is selected so that:
		84	## @iftex
		85	## @tex
		86	## $$ \Vert plist_{i} - plist_{i-1} \Vert < ptol $$
		87	## @end tex
		88	## @end iftex
		89	## @ifinfo
84	## @example	90	## @example
85	## is selected so that \|\| Plist@{ii@} - Plist@{ii-1@} \|\| < Ptol	91	## \|\| Plist@{i@} - Plist@{i-1@} \|\| < Ptol
86	## for ii=2:length(tvals)
87	## @end example	92	## @end example
88	## @end table	93	## @end ifinfo
		94	## for every @var{i} between 2 and length(@var{tvals}).
89	## @end deftypefn	95	## @end deftypefn
90		96
91	function [tvals, Plist] = dre (sys, Q, R, Qf, t0, tf, Ptol, maxits)	97	function [tvals, Plist] = dre (sys, Q, R, Qf, t0, tf, Ptol, maxits)

Lines 36-47 Link Here

(-)octave-2.1.58/scripts/control/base/impulse.m (-3 / +8 lines)
36	## the number of data values.	36	## the number of data values.
37	##	37	##
38	## Both parameters @var{tstop} and @var{n} can be omitted and will be	38	## Both parameters @var{tstop} and @var{n} can be omitted and will be
39	## computed from the eigenvalues of the A-Matrix.	39	## computed from the eigenvalues of the A Matrix.
40	## @end table	40	## @end table
41	## @strong{Outputs}	41	## @strong{Outputs}
42	## @var{y}, @var{t}: impulse response	42	## @table @var
		43	## @item y
		44	## Values of the impulse response.
		45	## @item t
		46	## Times of the impulse response.
		47	## @end table
43	## @end deftypefn	48	## @end deftypefn
44	## @seealso{step and __stepimp__}	49	## @seealso{step, __stepimp__}
45		50
46	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>	51	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
47	## Created: October 2, 1997	52	## Created: October 2, 1997

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(-)octave-2.1.58/scripts/control/base/lqg.m (-9 / +9 lines)
38	## intensities of independent Gaussian noise processes (as above)	38	## intensities of independent Gaussian noise processes (as above)
39	## @item q	39	## @item q
40	## @itemx r	40	## @itemx r
41	## state, control weighting respectively. Control ARE is	41	## state, control weighting respectively. Control @acronym{ARE} is
42	## @item in_idx	42	## @item in_idx
43	## names or indices of controlled inputs (see @code{sysidx}, @code{cellidx})	43	## names or indices of controlled inputs (see @command{sysidx}, @command{cellidx})
44	##	44	##
45	## default: last dim(R) inputs are assumed to be controlled inputs, all	45	## default: last dim(R) inputs are assumed to be controlled inputs, all
46	## others are assumed to be noise inputs.	46	## others are assumed to be noise inputs.
Lines 48-64 Link Here
48	## @strong{Outputs}	48	## @strong{Outputs}
49	## @table @var	49	## @table @var
50	## @item k	50	## @item k
51	## system data structure format LQG optimal controller (Obtain A,B,C	51	## system data structure format @acronym{LQG} optimal controller (Obtain A, B, C
52	## matrices with @code{sys2ss}, @code{sys2tf}, or @code{sys2zp} as	52	## matrices with @command{sys2ss}, @command{sys2tf}, or @command{sys2zp} as
53	## appropriate)	53	## appropriate).
54	## @item p1	54	## @item p1
55	## Solution of control (state feedback) algebraic Riccati equation	55	## Solution of control (state feedback) algebraic Riccati equation.
56	## @item q1	56	## @item q1
57	## Solution of estimation algebraic Riccati equation	57	## Solution of estimation algebraic Riccati equation.
58	## @item ee	58	## @item ee
59	## estimator poles	59	## Estimator poles.
60	## @item es	60	## @item es
61	## controller poles	61	## Controller poles.
62	## @end table	62	## @end table
63	## @end deftypefn	63	## @end deftypefn
64	## @seealso{h2syn, lqe, and lqr}	64	## @seealso{h2syn, lqe, and lqr}

Lines 17-37 Link Here

(-)octave-2.1.58/scripts/control/base/lsim.m (-13 / +11 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})	20	## @deftypefn {Function File} {[@var{y}, @var{x}] =} lsim (@var{sys}, @var{u}, @var{t}, @var{x0})
21	## Produce output for a linear simulation of a system	21	## Produce output for a linear simulation of a system; produces
		22	## a plot for the output of the system, @var{sys}.
22	##	23	##
23	## Produces a plot for the output of the system, sys.	24	## @var{u} is an array that contains the system's inputs. Each row in @var{u}
		25	## corresponds to a different time step. Each column in @var{u} corresponds to a
		26	## different input. @var{t} is an array that contains the time index of the
		27	## system; @var{t} should be regularly spaced. If initial conditions are required
		28	## on the system, the @var{x0} vector should be added to the argument list.
24	##	29	##
25	## U is an array that contains the system's inputs. Each row in u	30	## When the lsim function is invoked a plot is not displayed;
26	## corresponds to a different time step. Each column in u corresponds to a	31	## however, the data is returned in @var{y} (system output)
27	## different input. T is an array that contains the time index of the	32	## and @var{x} (system states).
28	## system. T should be regularly spaced. If initial conditions are required
29	## on the system, the x0 vector should be added to the argument list.
30	##
31	## When the lsim function is invoked with output parameters:
32	## [y,x] = lsim(sys,u,t,[x0])
33	## a plot is not displayed, however, the data is returned in y = system output
34	## and x = system states.
35	## @end deftypefn	33	## @end deftypefn
36		34
37	## Author: David Clem	35	## Author: David Clem

Lines 17-25 Link Here

(-)octave-2.1.58/scripts/control/base/ltifr.m (-6 / +17 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} ltifr (@var{a}, @var{b}, @var{w})	20	## @deftypefn {Function File} {@var{out} =} ltifr (@var{a}, @var{b}, @var{w})
21	## @deftypefnx {Function File} {} ltifr (@var{sys}, @var{w})	21	## @deftypefnx {Function File} {@var{out} =} ltifr (@var{sys}, @var{w})
22	## Linear time invariant frequency response of single input systems	22	## Linear time invariant frequency response of single-input systems.
		23	##
23	## @strong{Inputs}	24	## @strong{Inputs}
24	## @table @var	25	## @table @var
25	## @item a	26	## @item a
Lines 30-41 Link Here
30	## @item w	31	## @item w
31	## vector of frequencies	32	## vector of frequencies
32	## @end table	33	## @end table
33	## @strong{Outputs}	34	## @strong{Output}
34	## @var{out}	35	## @table @var
		36	## @item out
		37	## frequency response, that is:
		38	## @end table
		39	## @iftex
		40	## @tex
		41	## $$ G(j\omega) = (j\omega\,I-A)^{-1}B $$
		42	## @end tex
		43	## @end iftex
		44	## @ifinfo
35	## @example	45	## @example
36	## -1	46	## -1
37	## G(s) = (jw I-A) B	47	## G(s) = (jw I-A) B
38	## @end example	48	## @end example
		49	## @end ifinfo
39	## for complex frequencies @math{s = jw}.	50	## for complex frequencies @math{s = jw}.
40	## @end deftypefn	51	## @end deftypefn
41		52

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(-)octave-2.1.58/scripts/control/base/lyap.m (-5 / +5 lines)
21	## @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c})	21	## @deftypefn {Function File} {} lyap (@var{a}, @var{b}, @var{c})
22	## @deftypefnx {Function File} {} lyap (@var{a}, @var{b})	22	## @deftypefnx {Function File} {} lyap (@var{a}, @var{b})
23	## Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart	23	## Solve the Lyapunov (or Sylvester) equation via the Bartels-Stewart
24	## algorithm (Communications of the ACM, 1972).	24	## algorithm (Communications of the @acronym{ACM}, 1972).
25	##	25	##
26	## If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns	26	## If @var{a}, @var{b}, and @var{c} are specified, then @code{lyap} returns
27	## the solution of the Sylvester equation	27	## the solution of the Sylvester equation
Lines 35-45 Link Here
35	## a x + x b + c = 0	35	## a x + x b + c = 0
36	## @end example	36	## @end example
37	## @end ifinfo	37	## @end ifinfo
38	## If only @code{(a, b)} are specified, then @code{lyap} returns the	38	## If only @code{(a, b)} are specified, then @command{lyap} returns the
39	## solution of the Lyapunov equation	39	## solution of the Lyapunov equation
40	## @iftex	40	## @iftex
41	## @tex	41	## @tex
42	## $$ A^T X + X A + B = 0 $$	42	## $$ A^{ \rm T } X + X A + B = 0 $$
43	## @end tex	43	## @end tex
44	## @end iftex	44	## @end iftex
45	## @ifinfo	45	## @ifinfo
Lines 50-56 Link Here
50	## If @var{b} is not square, then @code{lyap} returns the solution of either	50	## If @var{b} is not square, then @code{lyap} returns the solution of either
51	## @iftex	51	## @iftex
52	## @tex	52	## @tex
53	## $$ A^T X + X A + B^T B = 0 $$	53	## $$ A^{ \rm T } X + X A + B^{ \rm T } B = 0 $$
54	## @end tex	54	## @end tex
55	## @end iftex	55	## @end iftex
56	## @ifinfo	56	## @ifinfo
Lines 62-68 Link Here
62	## or	62	## or
63	## @iftex	63	## @iftex
64	## @tex	64	## @tex
65	## $$ A X + X A^T + B B^T = 0 $$	65	## $$ A X + X A^{ \rm T } + B B^{ \rm T } = 0 $$
66	## @end tex	66	## @end tex
67	## @end iftex	67	## @end iftex
68	## @ifinfo	68	## @ifinfo

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(-)octave-2.1.58/scripts/control/base/nichols.m (-28 / +58 lines)
20	## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs})	20	## @deftypefn {Function File} {[@var{mag}, @var{phase}, @var{w}] =} nichols (@var{sys}, @var{w}, @var{outputs}, @var{inputs})
21	## Produce Nichols plot of a system.	21	## Produce Nichols plot of a system.
22	##	22	##
23	## inputs:	23	## @strong{Inputs}
24	## sys: system data structure (must be either purely continuous or discrete;	24	## @table @var
25	## see is_digital)	25	## @item sys
26	## w: frequency values for evaluation.	26	## System data structure (must be either purely continuous or discrete;
27	## if sys is continuous, then nichols evaluates G(jw)	27	## see @command{is_digital}).
28	## if sys is discrete, then nichols evaluates G(exp(jwT)), where T=sys.tsam	28	## @item w
29	## (the system sampling time)	29	## Frequency values for evaluation.
30	## default: the default frequency range is selected as follows: (These	30	## @itemize
31	## steps are NOT performed if w is specified)	31	## @item if sys is continuous, then nichols evaluates @math{G(jw)}.
32	## (1) via routine __bodquist__, isolate all poles and zeros away from	32	## @item if sys is discrete, then nichols evaluates @math{G(exp(jwT))},
33	## w=0 (jw=0 or exp(jwT)=1) and select the frequency	33	## where @var{T}=@var{sys}. @var{tsam} is the system sampling time.
34	## range based on the breakpoint locations of the frequencies.	34	## @item the default frequency range is selected as follows (These
35	## (2) if sys is discrete time, the frequency range is limited	35	## steps are @strong{not} performed if @var{w} is specified):
36	## to jwT in [0,2p*pi]	36	## @enumerate
37	## (3) A "smoothing" routine is used to ensure that the plot phase does	37	## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
38	## not change excessively from point to point and that singular	38	## @var{w}=0 (@math{jw=0} or @math{exp(jwT)=1}) and select the frequency range
39	## points (e.g., crossovers from +/- 180) are accurately shown.	39	## based on the breakpoint locations of the frequencies.
40	## outputs, inputs: the names or indices of the output(s) and input(s)	40	## @item if sys is discrete time, the frequency range is limited to jwT in
41	## to be used in the frequency response; see sysprune.	41	## @iftex
42	## outputs:	42	## @tex
43	## mag, phase: the magnitude and phase of the frequency response	43	## $ [0,~2p\,\pi] $.
44	## G(jw) or G(exp(jwT)) at the selected frequency values.	44	## @end tex
45	## w: the vector of frequency values used	45	## @end iftex
46	## If no output arguments are given, nichols plots the results to the screen.	46	## @ifinfo
47	## Descriptive labels are automatically placed. See xlabel, ylable, title,	47	## [0,2p*pi].
48	## and replot.	48	## @end ifinfo
		49	## @item A ``smoothing'' routine is used to ensure that the plot phase does
		50	## not change excessively from point to point and that singular points
		51	## (e.g., crossovers from +/- 180) are accurately shown.
		52	## @end enumerate
		53	## @end itemize
		54	## @item outputs
		55	## @itemx inputs
		56	## the names or indices of the output(s) and input(s) to be used in the
		57	## frequency response; see @command{sysprune}.
		58	## @end table
		59	## @strong{Outputs}
		60	## @table @var
		61	## @item mag
		62	## @itemx phase
		63	## The magnitude and phase of the frequency response @math{G(jw)} or
		64	## @math{G(exp(jwT))} at the selected frequency values.
		65	## @item w
		66	## The vector of frequency values used.
		67	## @end table
		68	## If no output arguments are given, @command{nichols} plots the results to the screen.
		69	## Descriptive labels are automatically placed. See @command{xlabel},
		70	## @command{ylabel}, @command{title}, and @command{replot}.
49	##	71	##
50	## Note: if the requested plot is for an MIMO system, mag is set to	72	## Note: if the requested plot is for an @acronym{MIMO} system, @var{mag} is set to
51	## \|\|G(jw)\|\| or \|\|G(exp(jwT))\|\| and phase information is not computed.	73	## @iftex
		74	## @tex
		75	## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
		76	## @end tex
		77	## @end iftex
		78	## @ifinfo
		79	## \|\|G(jw)\|\| or \|\|G(exp(jwT))\|\|
		80	## @end ifinfo
		81	## and phase information is not computed.
52	## @end deftypefn	82	## @end deftypefn
53		83
54	function [mag, phase, w] = nichols (sys, w, outputs, inputs)	84	function [mag, phase, w] = nichols (sys, w, outputs, inputs)

Lines 23-44 Link Here

(-)octave-2.1.58/scripts/control/base/nyquist.m (-17 / +22 lines)
23	## plot is printed to the screen.	23	## plot is printed to the screen.
24	##	24	##
25	## Compute the frequency response of a system.	25	## Compute the frequency response of a system.
		26	##
26	## @strong{Inputs} (pass as empty to get default values)	27	## @strong{Inputs} (pass as empty to get default values)
27	## @table @var	28	## @table @var
28	## @item sys	29	## @item sys
29	## system data structure (must be either purely continuous or discrete;	30	## system data structure (must be either purely continuous or discrete;
30	## see is_digital)	31	## see @code{is_digital})
31	## @item w	32	## @item w
32	## frequency values for evaluation.	33	## frequency values for evaluation.
33	## if sys is continuous, then bode evaluates @math{G(jw)}	34	## If sys is continuous, then bode evaluates @math{G(@var{jw})};
34	## if sys is discrete, then bode evaluates @math{G(exp(jwT))}, where	35	## if sys is discrete, then bode evaluates @math{G(exp(@var{jwT}))},
35	## @math{T} is the system sampling time.	36	## where @var{T} is the system sampling time.
36	## @item default	37	## @item default
37	## the default frequency range is selected as follows: (These	38	## the default frequency range is selected as follows: (These
38	## steps are NOT performed if @var{w} is specified)	39	## steps are @strong{not} performed if @var{w} is specified)
39	## @end table
40	## @enumerate	40	## @enumerate
41	## @item via routine __bodquist__, isolate all poles and zeros away from	41	## @item via routine @command{__bodquist__}, isolate all poles and zeros away from
42	## @var{w}=0 (@var{jw}=0 or @math{exp(@var{jwT})=1}) and select the frequency	42	## @var{w}=0 (@var{jw}=0 or @math{exp(@var{jwT})=1}) and select the frequency
43	## range based on the breakpoint locations of the frequencies.	43	## range based on the breakpoint locations of the frequencies.
44	## @item if @var{sys} is discrete time, the frequency range is limited	44	## @item if @var{sys} is discrete time, the frequency range is limited
Lines 47-63 Link Here
47	## [0,2p*pi]	47	## [0,2p*pi]
48	## @end ifinfo	48	## @end ifinfo
49	## @iftex	49	## @iftex
50	## $[0,2p*\pi]$	50	## @tex
		51	## $ [ 0,2 \, p \pi ] $
		52	## @end tex
51	## @end iftex	53	## @end iftex
52	## @item A "smoothing" routine is used to ensure that the plot phase does	54	## @item A ``smoothing'' routine is used to ensure that the plot phase does
53	## not change excessively from point to point and that singular	55	## not change excessively from point to point and that singular
54	## points (e.g., crossovers from +/- 180) are accurately shown.	56	## points (e.g., crossovers from +/- 180) are accurately shown.
55	## @end enumerate	57	## @end enumerate
56	## outputs, inputs: names or indices of the output(s) and input(s) to be
57	## used in the frequency response; see sysprune.
58	##
59	## @strong{Inputs} (pass as empty to get default values)
60	## @table @var
61	## @item atol	58	## @item atol
62	## for interactive nyquist plots: atol is a change-in-slope tolerance	59	## for interactive nyquist plots: atol is a change-in-slope tolerance
63	## for the of asymptotes (default = 0; 1e-2 is a good choice). This allows	60	## for the of asymptotes (default = 0; 1e-2 is a good choice). This allows
Lines 70-76 Link Here
70	## @itemx imagp	67	## @itemx imagp
71	## the real and imaginary parts of the frequency response	68	## the real and imaginary parts of the frequency response
72	## @math{G(jw)} or @math{G(exp(jwT))} at the selected frequency values.	69	## @math{G(jw)} or @math{G(exp(jwT))} at the selected frequency values.
73	## @item w	70	## @item w
74	## the vector of frequency values used	71	## the vector of frequency values used
75	## @end table	72	## @end table
76	##	73	##
Lines 79-87 Link Here
79	## interactively if they wish to zoom in (remove asymptotes)	76	## interactively if they wish to zoom in (remove asymptotes)
80	## Descriptive labels are automatically placed.	77	## Descriptive labels are automatically placed.
81	##	78	##
82	## Note: if the requested plot is for an MIMO system, a warning message is	79	## Note: if the requested plot is for an @acronym{MIMO} system, a warning message is
83	## presented; the returned information is of the magnitude	80	## presented; the returned information is of the magnitude
84	## \|\|G(jw)\|\| or \|\|G(exp(jwT))\|\| only; phase information is not computed.	81	## @iftex
		82	## @tex
		83	## $ \Vert G(jw) \Vert $ or $ \Vert G( {\rm exp}(jwT) \Vert $
		84	## @end tex
		85	## @end iftex
		86	## @ifinfo
		87	## \|\|G(jw)\|\| or \|\|G(exp(jwT))\|\|
		88	## @end ifinfo
		89	## only; phase information is not computed.
85	## @end deftypefn	90	## @end deftypefn
86		91
87	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>	92	## Author: R. Bruce Tenison <btenison@eng.auburn.edu>

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(-)octave-2.1.58/scripts/control/base/obsv.m (-6 / +16 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	##@deftypefn {Function File} {} obsv (@var{sys}, @var{c})	20	## @deftypefn {Function File} {} obsv (@var{sys}, @var{c})
21	## Build observability matrix	21	## @deftypefnx {Function File} {} obsv (@var{a}, @var{c})
		22	## Build observability matrix:
		23	## @iftex
		24	## @tex
		25	## $$ Q_b = \left[ \matrix{ C \cr
		26	## C\,A \cr
		27	## C\,A^2 \cr
		28	## \vdots \cr
		29	## C\,A^{n-1} } \right ] $$
		30	## @end tex
		31	## @end iftex
		32	## @ifinfo
22	## @example	33	## @example
23	## @group	34	## @group
24	## \| C \|	35	## \| C \|
Lines 28-38 Link Here
28	## \| CA^(n-1) \|	39	## \| CA^(n-1) \|
29	## @end group	40	## @end group
30	## @end example	41	## @end example
31	## of a system data structure or the pair (A, C).	42	## @end ifinfo
		43	## of a system data structure or the pair (@var{a}, @var{c}).
32	##	44	##
33	## Note: @code{obsv()} forms the observability matrix.	45	## The numerical properties of @command{is_observable}
34	##
35	## The numerical properties of is_observable()
36	## are much better for observability tests.	46	## are much better for observability tests.
37	## @end deftypefn	47	## @end deftypefn
38		48

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(-)octave-2.1.58/scripts/control/base/step.m (-3 / +8 lines)
36	## the number of data values.	36	## the number of data values.
37	##	37	##
38	## Both parameters @var{tstop} and @var{n} can be omitted and will be	38	## Both parameters @var{tstop} and @var{n} can be omitted and will be
39	## computed from the eigenvalues of the A-Matrix.	39	## computed from the eigenvalues of the A Matrix.
40	## @end table	40	## @end table
41	## @strong{Outputs}	41	## @strong{Outputs}
42	## @var{y}, @var{t}: impulse response	42	## @table @var
		43	## @item y
		44	## Values of the step response.
		45	## @item t
		46	## Times of the step response.
		47	## @end table
43	##	48	##
44	## When invoked with the output paramter y the plot is not displayed.	49	## When invoked with the output parameter @var{y} the plot is not displayed.
45	## @end deftypefn	50	## @end deftypefn
46	## @seealso{impulse and __stepimp__}	51	## @seealso{impulse and __stepimp__}
47		52

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(-)octave-2.1.58/scripts/control/base/tzero2.m (-5 / +5 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} tzero2 (@var{a}, @var{b}, @var{c}, @var{d}, @var{bal})	20	## @deftypefn {Function File} {@var{zr} =} tzero2 (@var{a}, @var{b}, @var{c}, @var{d}, @var{bal})
21	## Compute the transmission zeros of a, b, c, d.	21	## Compute the transmission zeros of @var{a}, @var{b}, @var{c}, @var{d}.
22	##	22	##
23	## bal = balancing option (see balance); default is "B".	23	## @var{bal} = balancing option (see balance); default is @code{"B"}.
24	##	24	##
25	## Needs to incorporate @code{mvzero} algorithm to isolate finite zeros; use	25	## Needs to incorporate @command{mvzero} algorithm to isolate finite zeros;
26	## @code{tzero} instead.	26	## use @command{tzero} instead.
27	## @end deftypefn	27	## @end deftypefn
28		28
29	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	29	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

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(-)octave-2.1.58/scripts/control/hinf/dgkfdemo.m (-1 / +10 lines)
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} dgkfdemo ()	20	## @deftypefn {Function File} {} dgkfdemo ()
21	## Octave Controls toolbox demo: H2/Hinfinity options demos	21	## Octave Controls toolbox demo:
		22	## @iftex
		23	## @tex
		24	## $ { \cal H }_2 $/$ { \cal H }_\infty $
		25	## @end tex
		26	## @end iftex
		27	## @ifinfo
		28	## H-2/H-infinity
		29	## @end ifinfo
		30	## options demos.
22	## @end deftypefn	31	## @end deftypefn
23		32
24	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	33	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

Lines 17-28 Link Here

(-)octave-2.1.58/scripts/control/hinf/h2norm.m (-5 / +22 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function Fil} {} h2norm (@var{sys})	20	## @deftypefn {Function File} {} h2norm (@var{sys})
21	## Computes the H2 norm of a system data structure (continuous time only)	21	## Computes the
		22	## @iftex
		23	## @tex
		24	## $ { \cal H }_2 $
		25	## @end tex
		26	## @end iftex
		27	## @ifinfo
		28	## H-2
		29	## @end ifinfo
		30	## norm of a system data structure (continuous time only).
22	##	31	##
23	## Reference:	32	## Reference:
24	## Doyle, Glover, Khargonekar, Francis, ``State Space Solutions to Standard	33	## Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions to Standard}
25	## H2 and Hinf Control Problems", IEEE TAC August 1989	34	## @iftex
		35	## @tex
		36	## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
		37	## @end tex
		38	## @end iftex
		39	## @ifinfo
		40	## @cite{H-2 and H-infinity}
		41	## @end ifinfo
		42	## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
26	## @end deftypefn	43	## @end deftypefn
27		44
28	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	45	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
Lines 50-56 function h2gain = h2norm (sys) Link Here
50	M = lyap (a,b*b');	67	M = lyap (a,b*b');
51	endif	68	endif
52	if( min(real(eig(M))) < 0)	69	if( min(real(eig(M))) < 0)
53	error("h2norm: grammian not >= 0 (lightly damped modes?)")	70	error("h2norm: gramian not >= 0 (lightly damped modes?)")
54	endif	71	endif
55		72
56	h2gain = sqrt(trace(d'd + cM*c'));	73	h2gain = sqrt(trace(d'd + cM*c'));

Lines 22-77 Link Here

(-)octave-2.1.58/scripts/control/hinf/hinfsyn.m (-22 / +67 lines)
22	## @strong{Inputs} input system is passed as either	22	## @strong{Inputs} input system is passed as either
23	## @table @var	23	## @table @var
24	## @item asys	24	## @item asys
25	## system data structure (see ss, sys2ss)	25	## system data structure (see @command{ss}, @command{sys2ss})
26	## @itemize @bullet	26	## @itemize @bullet
27	## @item controller is implemented for continuous time systems	27	## @item controller is implemented for continuous time systems
28	## @item controller is NOT implemented for discrete time systems (see	28	## @item controller is @strong{not} implemented for discrete time systems (see
29	## bilinear transforms in @code{c2d}, @code{d2c})	29	## bilinear transforms in @command{c2d}, @command{d2c})
30	## @end itemize	30	## @end itemize
31	## @item nu	31	## @item nu
32	## number of controlled inputs	32	## number of controlled inputs
33	## @item ny	33	## @item ny
34	## number of measured outputs	34	## number of measured outputs
35	## @item gmin	35	## @item gmin
36	## initial lower bound on H-infinity optimal gain	36	## initial lower bound on
		37	## @iftex
		38	## @tex
		39	## $ { \cal H }_\infty $
		40	## @end tex
		41	## @end iftex
		42	## @ifinfo
		43	## H-infinity
		44	## @end ifinfo
		45	## optimal gain
37	## @item gmax	46	## @item gmax
38	## initial upper bound on H-infinity optimal gain	47	## initial upper bound on
		48	## @iftex
		49	## @tex
		50	## $ { \cal H }_\infty $
		51	## @end tex
		52	## @end iftex
		53	## @ifinfo
		54	## H-infinity
		55	## @end ifinfo
		56	## Optimal gain.
39	## @item gtol	57	## @item gtol
40	## gain threshhold. Routine quits when gmax/gmin < 1+tol	58	## Gain threshold. Routine quits when @var{gmax}/@var{gmin} < 1+tol.
41	## @item ptol	59	## @item ptol
42	## poles with abs(real(pole)) < ptol*\|\|H\|\| (H is appropriate	60	## poles with @code{abs(real(pole))}
		61	## @iftex
		62	## @tex
		63	## $ < ptol \Vert H \Vert $
		64	## @end tex
		65	## @end iftex
		66	## @ifinfo
		67	## < ptol*\|\|H\|\|
		68	## @end ifinfo
		69	## (@var{H} is appropriate
43	## Hamiltonian) are considered to be on the imaginary axis.	70	## Hamiltonian) are considered to be on the imaginary axis.
44	## Default: 1e-9	71	## Default: 1e-9.
45	## @item tol	72	## @item tol
46	## threshhold for 0. Default: 200*eps	73	## threshold for 0. Default: 200*@code{eps}.
47	##	74	##
48	## @var{gmax}, @var{min}, @var{tol}, and @var{tol} must all be postive scalars.	75	## @var{gmax}, @var{min}, @var{tol}, and @var{tol} must all be postive scalars.
49	## @end table	76	## @end table
50	## @strong{Outputs}	77	## @strong{Outputs}
51	## @table @var	78	## @table @var
52	## @item k	79	## @item k
53	## system controller	80	## System controller.
54	## @item g	81	## @item g
55	## designed gain value	82	## Designed gain value.
56	## @item gw	83	## @item gw
57	## closed loop system	84	## Closed loop system.
58	## @item xinf	85	## @item xinf
59	## ARE solution matrix for regulator subproblem	86	## @acronym{ARE} solution matrix for regulator subproblem.
60	## @item yinf	87	## @item yinf
61	## ARE solution matrix for filter subproblem	88	## @acronym{ARE} solution matrix for filter subproblem.
62	## @end table	89	## @end table
63	##	90	##
		91	## References:
64	## @enumerate	92	## @enumerate
65	## @item Doyle, Glover, Khargonekar, Francis, "State Space Solutions	93	## @item Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions
66	## to Standard H2 and Hinf Control Problems," IEEE TAC August 1989	94	## to Standard}
		95	## @iftex
		96	## @tex
		97	## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
		98	## @end tex
		99	## @end iftex
		100	## @ifinfo
		101	## @cite{H-2 and H-infinity}
		102	## @end ifinfo
		103	## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
67	##	104	##
68	## @item Maciejowksi, J.M., "Multivariable feedback design,"	105	## @item Maciejowksi, J.M., @cite{Multivariable feedback design},
69	## Addison-Wesley, 1989, ISBN 0-201-18243-2	106	## Addison-Wesley, 1989, @acronym{ISBN} 0-201-18243-2.
70	##	107	##
71	## @item Keith Glover and John C. Doyle, "State-space formulae for all	108	## @item Keith Glover and John C. Doyle, @cite{State-space formulae for all
72	## stabilizing controllers that satisfy and h-infinity-norm bound	109	## stabilizing controllers that satisfy an}
73	## and relations to risk sensitivity,"	110	## @iftex
74	## Systems & Control Letters 11, Oct. 1988, pp 167-172.	111	## @tex
		112	## $ { \cal H }_\infty $@cite{norm}
		113	## @end tex
		114	## @end iftex
		115	## @ifinfo
		116	## @cite{H-infinity-norm}
		117	## @end ifinfo
		118	## @cite{bound and relations to risk sensitivity},
		119	## Systems & Control Letters 11, Oct. 1988, pp 167--172.
75	## @end enumerate	120	## @end enumerate
76	## @end deftypefn	121	## @end deftypefn
77		122

Lines 19-35 Link Here

(-)octave-2.1.58/scripts/control/hinf/is_dgkf.m (-10 / +18 lines)
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {[@var{retval}, @var{dgkf_struct} ] =} is_dgkf (@var{asys}, @var{nu}, @var{ny}, @var{tol} )	20	## @deftypefn {Function File} {[@var{retval}, @var{dgkf_struct} ] =} is_dgkf (@var{asys}, @var{nu}, @var{ny}, @var{tol} )
21	## Determine whether a continuous time state space system meets	21	## Determine whether a continuous time state space system meets
22	## assumptions of DGKF algorithm.	22	## assumptions of @acronym{DGKF} algorithm.
23	## Partitions system into:	23	## Partitions system into:
24	## @example	24	## @example
25	## [dx/dt] = [A \| Bw Bu ][w]	25	## [dx/dt] [A \| Bw Bu ][w]
26	## [ z ] [Cz \| Dzw Dzu ][u]	26	## [ z ] = [Cz \| Dzw Dzu ][u]
27	## [ y ] [Cy \| Dyw Dyu ]	27	## [ y ] [Cy \| Dyw Dyu ]
28	## @end example	28	## @end example
29	## or similar discrete-time system.	29	## or similar discrete-time system.
30	## If necessary, orthogonal transformations @var{qw}, @var{qz} and nonsingular	30	## If necessary, orthogonal transformations @var{qw}, @var{qz} and nonsingular
31	## transformations @var{ru}, @var{ry} are applied to respective vectors	31	## transformations @var{ru}, @var{ry} are applied to respective vectors
32	## @var{w}, @var{z}, @var{u}, @var{y} in order to satisfy DGKF assumptions.	32	## @var{w}, @var{z}, @var{u}, @var{y} in order to satisfy @acronym{DGKF} assumptions.
33	## Loop shifting is used if @var{dyu} block is nonzero.	33	## Loop shifting is used if @var{dyu} block is nonzero.
34	##	34	##
35	## @strong{Inputs}	35	## @strong{Inputs}
Lines 41-54 Link Here
41	## @item ny	41	## @item ny
42	## number of measured outputs	42	## number of measured outputs
43	## @item tol	43	## @item tol
44	## threshhold for 0. Default: 200@var{eps}	44	## threshold for 0; default: 200*@code{eps}.
45	## @end table	45	## @end table
46	## @strong{Outputs}	46	## @strong{Outputs}
47	## @table @var	47	## @table @var
48	## @item retval	48	## @item retval
49	## true(1) if system passes check, false(0) otherwise	49	## true(1) if system passes check, false(0) otherwise
50	## @item dgkf_struct	50	## @item dgkf_struct
51	## data structure of @code{is_dgkf} results. Entries:	51	## data structure of @command{is_dgkf} results. Entries:
52	## @table @var	52	## @table @var
53	## @item nw	53	## @item nw
54	## @itemx nz	54	## @itemx nz
Lines 84-98 Link Here
84	## @end table	84	## @end table
85	## @end table	85	## @end table
86	## @code{is_dgkf} exits with an error if the system is mixed	86	## @code{is_dgkf} exits with an error if the system is mixed
87	## discrete/continuous	87	## discrete/continuous.
88	##	88	##
89	## @strong{References}	89	## @strong{References}
90	## @table @strong	90	## @table @strong
91	## @item [1]	91	## @item [1]
92	## Doyle, Glover, Khargonekar, Francis, "State Space Solutions	92	## Doyle, Glover, Khargonekar, Francis, @cite{State Space Solutions to Standard}
93	## to Standard H2 and Hinf Control Problems," IEEE TAC August 1989	93	## @iftex
		94	## @tex
		95	## $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
		96	## @end tex
		97	## @end iftex
		98	## @ifinfo
		99	## @cite{H-2 and H-infinity}
		100	## @end ifinfo
		101	## @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
94	## @item [2]	102	## @item [2]
95	## Maciejowksi, J.M.: "Multivariable feedback design,"	103	## Maciejowksi, J.M., @cite{Multivariable Feedback Design}, Addison-Wesley, 1989.
96	## @end table	104	## @end table
97	## @end deftypefn	105	## @end deftypefn
98		106

Lines 17-34 Link Here

(-)octave-2.1.58/scripts/control/hinf/wgt1o.m (-8 / +27 lines)
17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.	17	## Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA.
18		18
19	## -- texinfo --	19	## -- texinfo --
20	## @deftypefn {Function File} {} wgt1o (@var{vl}, @var{vh}, @var{fc})	20	## @deftypefn {Function File} {@var{W} =} wgt1o (@var{vl}, @var{vh}, @var{fc})
21	## State space description of a first order weighting function.	21	## State space description of a first order weighting function.
22	##	22	##
23	## Weighting function are needed by the H2/H_infinity design procedure.	23	## Weighting function are needed by the
24	## These function are part of thye augmented plant P (see hinfdemo	24	## @iftex
25	## for an applicattion example).	25	## @tex
		26	## $ { \cal H }_2 / { \cal H }_\infty $
		27	## @end tex
		28	## @end iftex
		29	## @ifinfo
		30	## H-2/H-infinity
		31	## @end ifinfo
		32	## design procedure.
		33	## These function are part of the augmented plant @var{P}
		34	## (see @command{hinfdemo} for an application example).
26	##	35	##
27	## vl = Gain at low frequencies	36	## @strong{Inputs}
		37	## @table @var
		38	## @item vl
		39	## Gain at low frequencies.
		40	## @item vh
		41	## Gain at high frequencies.
		42	## @item fc
		43	## Corner frequency (in Hz, @strong{not} in rad/sec)
		44	## @end table
28	##	45	##
29	## vh = Gain at high frequencies	46	## @strong{Output}
30	##	47	## @table @var
31	## fc = Corner frequency (in Hz, not in rad/sec)	48	## @item W
		49	## Weighting function, given in form of a system data structure.
		50	## @end table
32	## @end deftypefn	51	## @end deftypefn
33		52
34	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>	53	## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>

Lines 20-39 Link Here

(-)octave-2.1.58/scripts/control/system/buildssic.m (-30 / +59 lines)
20	## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8})	20	## @deftypefn {Function File} {} buildssic (@var{clst}, @var{ulst}, @var{olst}, @var{ilst}, @var{s1}, @var{s2}, @var{s3}, @var{s4}, @var{s5}, @var{s6}, @var{s7}, @var{s8})
21	##	21	##
22	## Form an arbitrary complex (open or closed loop) system in	22	## Form an arbitrary complex (open or closed loop) system in
23	## state-space form from several systems. "@code{buildssic}" can	23	## state-space form from several systems. @command{buildssic} can
24	## easily (despite it's cryptic syntax) integrate transfer functions	24	## easily (despite its cryptic syntax) integrate transfer functions
25	## from a complex block diagram into a single system with one call.	25	## from a complex block diagram into a single system with one call.
26	## This function is especially useful for building open loop	26	## This function is especially useful for building open loop
27	## interconnections for H_infinity and H2 designs or for closing	27	## interconnections for
28	## loops with these controllers.	28	## @iftex
		29	## @tex
		30	## $ { \cal H }_\infty $ and $ { \cal H }_2 $
		31	## @end tex
		32	## @end iftex
		33	## @ifinfo
		34	## H-infinity and H-2
		35	## @end ifinfo
		36	## designs or for closing loops with these controllers.
29	##	37	##
30	## Although this function is general purpose, the use of "@code{sysgroup}"	38	## Although this function is general purpose, the use of @command{sysgroup}
31	## "@code{sysmult}", "@code{sysconnect}" and the like is recommended for	39	## @command{sysmult}, @command{sysconnect} and the like is recommended for
32	## standard operations since they can handle mixed discrete and continuous	40	## standard operations since they can handle mixed discrete and continuous
33	## systems and also the names of inputs, outputs, and states.	41	## systems and also the names of inputs, outputs, and states.
34	##	42	##
35	## The parameters consist of 4 lists that describe the connections	43	## The parameters consist of 4 lists that describe the connections
36	## outputs and inputs and up to 8 systems s1-s8.	44	## outputs and inputs and up to 8 systems @var{s1}--@var{s8}.
37	## Format of the lists:	45	## Format of the lists:
38	## @table @var	46	## @table @var
39	## @item clst	47	## @item clst
Lines 42-68 Link Here
42	## equal to the sum of all inputs of s1-s8.	50	## equal to the sum of all inputs of s1-s8.
43	##	51	##
44	## Example:	52	## Example:
45	## @code{[1 2 -1; 2 1 0]} ==> new input 1 is old inpout 1	53	## @code{[1 2 -1; 2 1 0]} means that: new input 1 is old input 1
46	## + output 2 - output 1, new input 2 is old input 2	54	## + output 2 - output 1, and new input 2 is old input 2
47	## + output 1. The order of rows is arbitrary.	55	## + output 1. The order of rows is arbitrary.
48	##	56	##
49	## @item ulst	57	## @item ulst
50	## if not empty the old inputs in vector Ulst will	58	## if not empty the old inputs in vector @var{ulst} will
51	## be appended to the outputs. You need this if you	59	## be appended to the outputs. You need this if you
52	## want to "pull out" the input of a system. Elements	60	## want to ``pull out'' the input of a system. Elements
53	## are input numbers of s1-s8.	61	## are input numbers of @var{s1}--@var{s8}.
54	##	62	##
55	## @item olst	63	## @item olst
56	## output list, specifiy the outputs of the resulting	64	## output list, specifiy the outputs of the resulting
57	## systems. Elements are output numbers of s1-s8.	65	## systems. Elements are output numbers of @var{s1}--@var{s8}.
58	## The numbers are alowed to be negative and may	66	## The numbers are allowed to be negative and may
59	## appear in any order. An empty matrix means	67	## appear in any order. An empty matrix means
60	## all outputs.	68	## all outputs.
61	##	69	##
62	## @item ilst	70	## @item ilst
63	## input list, specifiy the inputs of the resulting	71	## input list, specifiy the inputs of the resulting
64	## systems. Elements are input numbers of s1-s8.	72	## systems. Elements are input numbers of @var{s1}--@var{s8}.
65	## The numbers are alowed to be negative and may	73	## The numbers are allowed to be negative and may
66	## appear in any order. An empty matrix means	74	## appear in any order. An empty matrix means
67	## all inputs.	75	## all inputs.
68	## @end table	76	## @end table
Lines 82-101 Link Here
82	## @end group	90	## @end group
83	## @end example	91	## @end example
84	##	92	##
85	## The closed loop system GW can be optained by	93	## The closed loop system @var{GW} can be optained by
86	## @example	94	## @example
87	## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K);	95	## GW = buildssic([1 2; 2 -1], 2, [1 2 3], 2, G, K);
88	## @end example	96	## @end example
89	## @table @var	97	## @table @var
90	## @item clst	98	## @item clst
91	## (1. row) connect input 1 (G) with output 2 (K).	99	## 1st row: connect input 1 (@var{G}) with output 2 (@var{K}).
92	## (2. row) connect input 2 (K) with neg. output 1 (G).	100	##
		101	## 2nd row: connect input 2 (@var{K}) with negative output 1 (@var{G}).
93	## @item ulst	102	## @item ulst
94	## append input of (2) K to the number of outputs.	103	## Append input of 2 (@var{K}) to the number of outputs.
95	## @item olst	104	## @item olst
96	## Outputs are output of 1 (G), 2 (K) and appended output 3 (from Ulst).	105	## Outputs are output of 1 (@var{G}), 2 (@var{K}) and
		106	## appended output 3 (from @var{ulst}).
97	## @item ilst	107	## @item ilst
98	## the only input is 2 (K).	108	## The only input is 2 (@var{K}).
99	## @end table	109	## @end table
100	##	110	##
101	## Here is a real example:	111	## Here is a real example:
Lines 104-111 Link Here
104	## +----+	114	## +----+
105	## -------------------->\| W1 \|---> v1	115	## -------------------->\| W1 \|---> v1
106	## z \| +----+	116	## z \| +----+
107	## ----\|-------------+ \|\| GW \|\| => min.	117	## ----\|-------------+
108	## \| \| vz infty	118	## \| \|
109	## \| +---+ v +----+	119	## \| +---+ v +----+
110	## --->\| G \|--->O---->\| W2 \|---> v2	120	## --->\| G \|--->O---->\| W2 \|---> v2
111	## \| +---+ \| +----+	121	## \| +---+ \| +----+
Lines 114-127 Link Here
114	## u y	124	## u y
115	## @end group	125	## @end group
116	## @end example	126	## @end example
		127	## @iftex
		128	## @tex
		129	## $$ { \rm min } \Vert GW_{vz} \Vert _\infty $$
		130	## @end tex
		131	## @end iftex
		132	## @ifinfo
		133	## @example
		134	## min \|\| GW \|\|
		135	## vz infty
		136	## @end example
		137	## @end ifinfo
117	##	138	##
118	## The closed loop system GW from [z; u]' to [v1; v2; y]' can be	139	## The closed loop system @var{GW}
119	## obtained by (all SISO systems):	140	## @iftex
		141	## @tex
		142	## from $ [z,~u]^{ \rm T } $ to $ [v_1,~v_2,~y]^{ \rm T } $
		143	## @end tex
		144	## @end iftex
		145	## @ifinfo
		146	## from [z, u]' to [v1, v2, y]'
		147	## @end ifinfo
		148	## can be obtained by (all @acronym{SISO} systems):
120	## @example	149	## @example
121	## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5],	150	## GW = buildssic([1, 4; 2, 4; 3, 1], 3, [2, 3, 5],
122	## [3, 4], G, W1, W2, One);	151	## [3, 4], G, W1, W2, One);
123	## @end example	152	## @end example
124	## where "One" is a unity gain (auxillary) function with order 0.	153	## where ``One'' is a unity gain (auxillary) function with order 0.
125	## (e.g. @code{One = ugain(1);})	154	## (e.g. @code{One = ugain(1);})
126	## @end deftypefn	155	## @end deftypefn
127		156

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(-)octave-2.1.58/scripts/control/system/c2d.m (-21 / +45 lines)
20	## @deftypefn {Function File} {} c2d (@var{sys}, @var{opt}, @var{t})	20	## @deftypefn {Function File} {} c2d (@var{sys}, @var{opt}, @var{t})
21	## @deftypefnx {Function File} {} c2d (@var{sys}, @var{t})	21	## @deftypefnx {Function File} {} c2d (@var{sys}, @var{t})
22	##	22	##
		23	## Converts the system data structure describing:
		24	## @iftex
		25	## @tex
		26	## $$ \dot x = A_c\,x + B_c\,u $$
		27	## @end tex
		28	## @end iftex
		29	## @ifinfo
		30	## @example
		31	## .
		32	## x = Ac x + Bc u
		33	## @end example
		34	## @end ifinfo
		35	## into a discrete time equivalent model:
		36	## @iftex
		37	## @tex
		38	## $$ x_{n+1} = A_d\,x_n + B_d\,u_n $$
		39	## @end tex
		40	## @end iftex
		41	## @ifinfo
		42	## @example
		43	## x[n+1] = Ad x[n] + Bd u[n]
		44	## @end example
		45	## @end ifinfo
		46	## via the matrix exponential or bilinear transform.
		47	##
23	## @strong{Inputs}	48	## @strong{Inputs}
24	## @table @var	49	## @table @var
25	## @item sys	50	## @item sys
Lines 33-70 Link Here
33	## use the matrix exponential (default)	58	## use the matrix exponential (default)
34	## @item "bi"	59	## @item "bi"
35	## use the bilinear transformation	60	## use the bilinear transformation
36	## @end table	61	## @iftex
		62	## @tex
		63	## $$ s = { 2\,(z-1) \over T\,(z+1) } $$
		64	## @end tex
		65	## @end iftex
		66	## @ifinfo
37	## @example	67	## @example
38	## 2(z-1)	68	## 2(z-1)
39	## s = -----	69	## s = -----
40	## T(z+1)	70	## T(z+1)
41	## @end example	71	## @end example
		72	## @end ifinfo
42	## FIXME: This option exits with an error if @var{sys} is not purely	73	## FIXME: This option exits with an error if @var{sys} is not purely
43	## continuous. (The @code{ex} option can handle mixed systems.)	74	## continuous. (The @code{ex} option can handle mixed systems.)
44	## @item t
45	## sampling time; required if sys is purely continuous.
46	##
47	## If the 2nd argument is not a string, @code{c2d} assumes that
48	## the 2nd argument is @var{t} and performs appropriate argument checks.
49	## @item "matched"	75	## @item "matched"
50	## Use the matched pole/zero equivalent transformation (currently only	76	## Use the matched pole/zero equivalent transformation (currently only
51	## works for purely continuous SISO systems).	77	## works for purely continuous @acronym{SISO} systems).
		78	## @end table
		79	## @item t
		80	## sampling time; required if @var{sys} is purely continuous.
		81	##
		82	## @strong{Note:} if the second argument is not a string, @code{c2d()}
		83	## assumes that the second argument is @var{t} and performs
		84	## appropriate argument checks.
52	## @end table	85	## @end table
53	##	86	##
54	## @strong{Outputs}	87	## @strong{Output}
55	## @var{dsys} discrete time equivalent via zero-order hold,	88	## @table @var
56	## sample each @var{t} sec.	89	## @item dsys
57	##	90	## Discrete time equivalent via zero-order hold, sample each @var{t} sec.
58	## converts the system data structure describing	91	## @end table
59	## @example
60	## .
61	## x = Ac x + Bc u
62	## @end example
63	## into a discrete time equivalent model
64	## @example
65	## x[n+1] = Ad x[n] + Bd u[n]
66	## @end example
67	## via the matrix exponential or bilinear transform
68	##	92	##
69	## This function adds the suffix @code{_d}	93	## This function adds the suffix @code{_d}
70	## to the names of the new discrete states.	94	## to the names of the new discrete states.

Lines 21-32 Link Here

(-)octave-2.1.58/scripts/control/system/is_observable.m (-2 / +2 lines)
21	## @deftypefnx {Function File} {[@var{retval}, @var{u}] =} is_observable (@var{sys}, @var{tol})	21	## @deftypefnx {Function File} {[@var{retval}, @var{u}] =} is_observable (@var{sys}, @var{tol})
22	## Logical check for system observability.	22	## Logical check for system observability.
23	##	23	##
24	## Default: tol = 10norm(a,'fro')eps	24	## Default: tol = @code{tol = 10norm(a,'fro')eps}
25	##	25	##
26	## Returns 1 if the system @var{sys} or the pair (@var{a}, @var{c}) is	26	## Returns 1 if the system @var{sys} or the pair (@var{a}, @var{c}) is
27	## observable, 0 if not.	27	## observable, 0 if not.
28	##	28	##
29	## @strong{See} @code{is_controllable} for detailed description of arguments	29	## See @command{is_controllable} for detailed description of arguments
30	## and default values.	30	## and default values.
31	## @end deftypefn	31	## @end deftypefn
32	## @seealso{size, rows, columns, length, ismatrix, isscalar, and isvector}	32	## @seealso{size, rows, columns, length, ismatrix, isscalar, and isvector}

Lines 1-3 Link Here

(-)octave-2.1.58/scripts/control/system/is_stabilizable.m (-8 / +17 lines)
		1	## Copyright (C) 1998 Kai P. Mueller.
		2	##
1	## This file is part of Octave.	3	## This file is part of Octave.
2	##	4	##
3	## Octave is free software; you can redistribute it and/or modify it	5	## Octave is free software; you can redistribute it and/or modify it
Lines 19-33 Link Here
19	## @deftypefnx {Function File} {@var{retval} =} is_stabilizable (@var{a}, @var{b}, @var{tol}, @var{dflg})	21	## @deftypefnx {Function File} {@var{retval} =} is_stabilizable (@var{a}, @var{b}, @var{tol}, @var{dflg})
20	## Logical check for system stabilizability (i.e., all unstable modes are controllable).	22	## Logical check for system stabilizability (i.e., all unstable modes are controllable).
21	## Returns 1 if the system is stabilizable, 0 if the the system is not stabilizable, -1	23	## Returns 1 if the system is stabilizable, 0 if the the system is not stabilizable, -1
22	## if the system has non stabilizable modes at the imaginary axis (unit circle for discrete-time	24	## if the system has non stabilizable modes at the imaginary axis (unit circle for
23	## systems.	25	## discrete-time systems.
24	##
25	## Test for stabilizability is performed via Hautus Lemma. If @var{dflg}!=0 assume that
26	## discrete-time matrices (a,b) are supplied.
27	##	26	##
28		27	## Test for stabilizability is performed via Hautus Lemma. If
29	## See also: size, rows, columns, length, ismatrix, isscalar, isvector	28	## @iftex
30	## is_observable, is_stabilizable, is_detectable	29	## @tex
		30	## @var{dflg}$\neq$0
		31	## @end tex
		32	## @end iftex
		33	## @ifinfo
		34	## @var{dflg}!=0
		35	## @end ifinfo
		36	## assume that discrete-time matrices (a,b) are supplied.
		37	## @end deftypefn
		38	## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector
		39	## is_observable, is_stabilizable, is_detectable}
31		40
32	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>	41	## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
33	## Created: August 1993	42	## Created: August 1993

Lines 20-27 Link Here

(-)octave-2.1.58/scripts/control/system/sys2ss.m (-11 / +14 lines)
20	## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{yd}] =} sys2ss (@var{sys})	20	## @deftypefn {Function File} {[@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{yd}] =} sys2ss (@var{sys})
21	## Extract state space representation from system data structure.	21	## Extract state space representation from system data structure.
22	##	22	##
23	## @strong{Inputs}	23	## @strong{Input}
24	## @var{sys} system data structure	24	## @table @var
		25	## @item sys
		26	## System data structure.
		27	## @end table
25	##	28	##
26	## @strong{Outputs}	29	## @strong{Outputs}
27	## @table @var	30	## @table @var
Lines 29-57 Link Here
29	## @itemx b	32	## @itemx b
30	## @itemx c	33	## @itemx c
31	## @itemx d	34	## @itemx d
32	## state space matrices for sys	35	## State space matrices for @var{sys}.
33	##	36	##
34	## @item tsam	37	## @item tsam
35	## sampling time of sys (0 if continuous)	38	## Sampling time of @var{sys} (0 if continuous).
36	##	39	##
37	## @item n	40	## @item n
38	## @itemx nz	41	## @itemx nz
39	## number of continuous, discrete states (discrete states come	42	## Number of continuous, discrete states (discrete states come
40	## last in state vector @var{x})	43	## last in state vector @var{x}).
41	##	44	##
42	## @item stname	45	## @item stname
43	## @itemx inname	46	## @itemx inname
44	## @itemx outname	47	## @itemx outname
45	## signal names (lists of strings); names of states,	48	## Signal names (lists of strings); names of states,
46	## inputs, and outputs, respectively	49	## inputs, and outputs, respectively.
47	##	50	##
48	## @item yd	51	## @item yd
49	## binary vector; @var{yd}(@var{ii}) is 1 if output @var{y}(@var{ii})$	52	## Binary vector; @var{yd}(@var{ii}) is 1 if output @var{y}(@var{ii})
50	## is discrete (sampled); otherwise @var{yd}(@var{ii}) 0.	53	## is discrete (sampled); otherwise @var{yd}(@var{ii}) is 0.
51	##	54	##
52	## @end table	55	## @end table
53	## A warning massage is printed if the system is a mixed	56	## A warning massage is printed if the system is a mixed
54	## continuous and discrete system	57	## continuous and discrete system.
55	##	58	##
56	## @strong{Example}	59	## @strong{Example}
57	## @example	60	## @example