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 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)
## x = lyap (a, 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, c) are specified, then lyap returns the solution of the
## Lyapunov equation
##
## a x + x a' + c = 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) or lyap (a, 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';
c = b;
b = a';
else
## Try to solve a'x + x a + b' b = 0.
m = columns (b);
c = b' * b;
b = a;
a = a';
endif
if (m != n)
error ("lyap: a, b not conformably dimensioned");
endif
else
## If you share your installation of Octave with others, you
## shouldn't remove the following code. Instead, users should
## add
##
## global __disable_lyap_interface_change_warning__;
##
## to their personal ~/.octaverc files. This warning will likely
## disappear for good in some future version of Octave.
if (! exist ("__disable_lyap_interface_change_warning__"))
global __disable_lyap_interface_change_warning__;
warning ("for compatibility with Matlab, lyap now computes");
warning ("");
warning (" A*X + X*A' + C = 0");
warning ("");
warning ("instead of");
warning ("");
warning (" A'*X + X*A + C = 0");
warning ("");
warning ("as in previous versions");
warning ("");
warning ("to completely disable this message, put")
warning ("")
warning (" global __disable_lyap_interface_change_warning__;");
warning ("")
warning ("in your ~/.octaverc file")
endif
c = b;
b = a';
endif
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
|
