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is_stabl.m
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1999-04-29
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# Copyright (C) 1993, 1994, 1995 John W. Eaton
#
# This file is part of Octave.
#
# Octave is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version.
#
# Octave is distributed in the hope that it will be useful, but WITHOUT
# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License
# along with Octave; see the file COPYING. If not, write to the Free
# Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
function retval = is_stabl (a, tol, disc)
# Usage: retval = is_stabl (a {,tol,disc})
# or retval = is_stabl (sys{,tol})
#
# Returns retval = 1 if the matrix a or the system a is stable, or 0 if not.
#
# tol is a roundoff paramter, set to 200*eps if omitted.
# disc != 0: stable if eig(a) in unit circle
# 0: stable if eig(a) in open LHP (default)
#
# See also: size, rows, columns, length, is_mat, is_scal, is_vec
# is_obsrv, is_stabi, is_detec, krylov, krylovb
# Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993.
# Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for systems
# Updated to simpler form by a.s.hodel 1998
if( (nargin < 1) | (nargin > 3) ) usage("is_stabl(a {,tol,disc})");
elseif(is_struct(a))
# system was passed
if(nargin < 3) disc = is_digit(a);
elseif(disc != is_digit(a))
warning("is_stabl: disc =%d does not match system",disc)
endif
sys = sysupdat(a,"ss");
a = sys2ss(sys);
else
if(nargin < 3) disc = 0; endif
if(is_sqr(a) == 0)
error("A(%dx%d) must be square",rows(A), columns(A));
endif
endif
if(nargin < 2) tol = 200*eps;
elseif( !is_scal(tol) )
error("is_stabl: tol(%dx%d) must be a scalar",rows(tol),columns(tol));
endif
l = eig(a);
if(disc) nbad = sum(abs(l)*(1+tol) > 1);
else nbad = sum(real(l)+tol > 0); endif
retval = (nbad == 0);
endfunction