Mercurial > hg > octave-nkf
diff scripts/control/is_controllable.m @ 3346:8dd4718801fd
[project @ 1999-11-09 18:18:12 by jwe]
author | jwe |
---|---|
date | Tue, 09 Nov 1999 18:18:37 +0000 |
parents | f7e4a95916f2 |
children | 69b167451491 |
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--- a/scripts/control/is_controllable.m +++ b/scripts/control/is_controllable.m @@ -16,24 +16,49 @@ # along with Octave; see the file COPYING. If not, write to the Free # Software Foundation, 59 Temple Place, Suite 330, Boston, MA 02111 USA. -function [retval,U] = is_controllable (a, b, tol) -# [retval, U] = is_controllable (a, b {,tol}) -# = is_controllable (sys{, tol}) -# Returns retval=1 if the system sys or the pair (a, b) is controllable -# 0 if not. -# U is an orthogonal basis of the controllable subspace. -# -# Controllability is determined by applying Arnoldi iteration with -# complete re-orthogonalization to obtain an orthogonal basis of the -# Krylov subspace. -# -# span ([b,a*b,...,a^ b]). -# -# tol is a roundoff paramter, set to 10*eps if omitted. -# +## -*- texinfo -*- +## @deftypefn {Function File } {[@var{retval}, @var{U}] =} is_controllable (@var{sys}@{, @var{tol}@}) +## @deftypefnx {Function File } {[@var{retval}, @var{U}] =} is_controllable (@var{a}@{, @var{b} ,@var{tol}@}) +## Logical check for system controllability. +## +## @strong{Inputs} +## @table @var +## @item sys +## system data structure +## @item a, b +## @var{n} by @var{n}, @var{n} by @var{m} matrices, respectively +## @item tol +## optional roundoff paramter. default value: @code{10*eps} +## @end table +## +## @strong{Outputs} +## @table @var +## @item retval +## Logical flag; returns true (1) if the system @var{sys} or the +## pair (@var{a},@var{b}) is controllable, whichever was passed as input arguments. +## @item U +## U is an orthogonal basis of the controllable subspace. +## @end table +## +## @strong{Method} +## Controllability is determined by applying Arnoldi iteration with +## complete re-orthogonalization to obtain an orthogonal basis of the +## Krylov subspace +## @example +## span ([b,a*b,...,a^@{n-1@}*b]). +## @end example +## The Arnoldi iteration is executed with @code{krylov} if the system has a single input; otherwise a block Arnoldi iteration is performed with @code{krylovb}. +## +## @strong{See also} +## @code{is_observable}, @code{is_stabilizable}, @code{is_detectable}, +## @code{krylov}, @code{krylovb} +## +## @end deftypefn + # See also: size, rows, columns, length, is_matrix, is_scalar, is_vector # is_observable, is_stabilizable, is_detectable, krylov, krylovb +function [retval,U] = is_controllable (a, b, tol) # Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993. # Updated by A. S. Hodel (scotte@eng.auburn.edu) Aubust, 1995 to use krylovb # Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for packed systems