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lyap.m
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1999-03-05
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## Copyright (C) 1996, 1997 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, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## Usage: x = lyap (a, b {,c})
##
## If (a, b, c) are specified, then lyap returns the solution of the
## Sylvester equation
##
## a x + x b + c = 0
##
## If only (a, b) are specified, then lyap returns the solution of the
## Lyapunov equation
##
## a' x + x a + b = 0
##
## If b is not square, then lyap returns the solution of either
##
## a' x + x a + b' b = 0
##
## or
##
## a x + x a' + b b' = 0
##
## whichever is appropriate.
##
## Solves by using the Bartels-Stewart algorithm (1972).
## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe
function x = lyap (a, b, c)
if (nargin != 3 && nargin != 2)
usage ("lyap (a, b {,c})");
endif
if ((n = is_square(a)) == 0)
error ("lyap: a is not square");
endif
if (nargin == 2)
## Transform Lyapunov equation to Sylvester equation form.
if ((m = is_square (b)) == 0)
if ((m = rows (b)) == n)
## solve a x + x a' + b b' = 0
b = b * b';
a = a';
else
## Try to solve a'x + x a + b' b = 0.
m = columns (b);
b = b' * b;
endif
if (m != n)
error ("lyap: a, b not conformably dimensioned");
endif
endif
## Set up Sylvester equation.
c = b;
b = a;
a = b';
else
## Check dimensions.
if ((m = is_square (b)) == 0)
error ("lyap: b must be square in a sylvester equation");
endif
[n1, m1] = size(c);
if (n != n1 || m != m1)
error("lyap: a,b,c not conformably dimensioned");
endif
endif
## Call octave built-in function.
x = syl (a, b, c);
endfunction