1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
|
## Copyright (C) 1996, 1997, 2000, 2002, 2004, 2005, 2006, 2007
## Auburn University. All rights reserved.
##
##
## This program 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 3 of the License, or (at
## your option) any later version.
##
## This program 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 this program; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @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
## @iftex
## @tex
## $$ A X + X B + C = 0 $$
## @end tex
## @end iftex
## @ifinfo
## @example
## 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
## $$ A^T X + X A + B = 0 $$
## @end tex
## @end iftex
## @ifinfo
## @example
## a' x + x a + b = 0
## @end example
## @end ifinfo
## If @var{b} is not square, then @code{lyap} returns the solution of either
## @iftex
## @tex
## $$ A^T X + X A + B^T B = 0 $$
## @end tex
## @end iftex
## @ifinfo
## @example
## a' x + x a + b' b = 0
## @end example
## @end ifinfo
## @noindent
## or
## @iftex
## @tex
## $$ A X + X A^T + B B^T = 0 $$
## @end tex
## @end iftex
## @ifinfo
## @example
## a x + x a' + b b' = 0
## @end example
## @end ifinfo
## @noindent
## whichever is appropriate.
##
## Solves by using the Bartels-Stewart algorithm (1972).
## @end deftypefn
## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe
function x = lyap (a, b, c)
if (nargin != 3 && nargin != 2)
print_usage ();
endif
if ((n = issquare(a)) == 0)
error ("lyap: a is not square");
endif
if (nargin == 2)
## Transform Lyapunov equation to Sylvester equation form.
if ((m = issquare (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 = issquare (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
|
