Mercurial > hg > octave-nkf
diff scripts/control/is_stabilizable.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_stabilizable.m +++ b/scripts/control/is_stabilizable.m @@ -16,25 +16,32 @@ # 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_stabilizable (a, b, tol) +## -*- texinfo -*- +## @deftypefn {Function File } {[@var{retval}, @var{U}] =} is_stabilizable (@var{sys}@{, @var{tol}@}) +## @deftypefnx {Function File } {[@var{retval}, @var{U}] =} is_stabilizable (@var{a}@{, @var{b} ,@var{tol}@}) +## Logical check for system stabilizability (i.e., all unstable modes are controllable). +## +## +## Test for stabilizability is performed via an ordered Schur decomposition +## that reveals the unstable subspace of the system @var{A} matrix. +## +## Returns @code{retval} = 1 if the system, @code{a}, is stabilizable, if the pair +## (@code{a}, @code{b}) is stabilizable, or 0 if not. +## @code{U} = orthogonal basis of controllable subspace. +## +## Controllable subspace 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^ b]). +## @end example +## tol is a roundoff paramter, set to 200*eps if omitted. +## @end deftypefn -# Usage: [retval,U] = is_stabilizable (a {, b, tol}) -# -# Returns retval = 1 if the system, a, is stabilizable, if the pair (a, b) is -# stabilizable, or 0 if not. -# U = orthogonal basis of controllable subspace. -# -# Controllable subspace 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 200*eps if omitted. -# -# See also: size, rows, columns, length, is_matrix, is_scalar, is_vector -# is_observable, is_stabilizable, is_detectable +## See also: size, rows, columns, length, is_matrix, is_scalar, is_vector +## is_observable, is_stabilizable, is_detectable +function [retval,U] = is_stabilizable (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 to accept systems