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comparison scripts/control/lyap.m @ 53:4565ad8b4697

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[project @ 1993-08-11 21:21:34 by jwe]
author jwe
date Wed, 11 Aug 1993 21:21:34 +0000
parents adade67872a7
children 8d4431f4a00a
comparison
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52:9eda1009cf95 53:4565ad8b4697
1 function x = lyap(a,b,c) 1 function x = lyap (a, b, c)
2 2
3 % usage: x = lyap(a,b{,c}) 3 # usage: x = lyap (a, b {,c})
4 % 4 #
5 % If (a,b,c) are specified, then lyap returns the solution of the Sylvester 5 # If (a, b, c) are specified, then lyap returns the solution of the
6 % equation 6 # Sylvester equation
7 % a x + x b + c = 0 7 #
8 % 8 # a x + x b + c = 0
9 % If only (a,b) are specified, then lyap returns the solution of the 9 #
10 % Lyapunov equation 10 # If only (a, b) are specified, then lyap returns the solution of the
11 % a' x + x a + b = 0 11 # Lyapunov equation
12 % If b is not square, then lyap returns the solution of either 12 #
13 % a' x + x a + b' b = 0 13 # a' x + x a + b = 0
14 % or 14 #
15 % a x + x a' + b b' = 0 15 # If b is not square, then lyap returns the solution of either
16 % whichever is appropriate. 16 #
17 # a' x + x a + b' b = 0
18 #
19 # or
20 #
21 # a x + x a' + b b' = 0
22 #
23 # whichever is appropriate.
17 24
18 if((nargin ~= 3) && (nargin ~= 2)) 25 if (nargin != 3 && nargin != 2)
19 error("lyap: illegal number of arguments") 26 error ("lyap: illegal number of arguments");
20 return 27 return;
21 endif 28 endif
22 29
23 if( (n = is_square(a)) == 0 ) 30 if ((n = is_square(a)) == 0)
24 error("lyap: a is not square"); 31 error ("lyap: a is not square");
25 return 32 return;
26 endif 33 endif
27 34
28 if(nargin == 2) 35 if (nargin == 2)
29 disp('LYAP') 36
30 a=a 37 # Transform Lyapunov equation to Sylvester equation form.
31 b=b 38
32 % transform Lyapunov equation to Sylvester equation form 39 if ((m = is_square (b)) == 0)
33 if ( (m=is_square(b)) == 0) 40 if ((m = rows (b)) == n)
34 if( (m=rows(b)) == n) 41
35 disp('TYPE CONTROL') 42 # solve a x + x a' + b b' = 0
36 % solve a x + x a' + b b' = 0 43
37 b = b*b'; 44 b = b * b';
38 a = a'; 45 a = a';
39 else 46 else
40 disp('TYPE OBSERVE') 47
41 % (try to ) solve a'x + x a + b' b = 0 48 # Try to solve a'x + x a + b' b = 0.
42 m = columns(b); 49
43 b = b'*b; 50 m = columns (b);
51 b = b' * b;
52 endif
53
54 if (m != n)
55 error ("lyap: a, b not conformably dimensioned");
56 return;
57 endif
44 endif 58 endif
45 if(m ~= n) 59
46 error("lyap: a, b not conformably dimensioned"); 60 # Set up Sylvester equation.
61
62 c = b;
63 b = a;
64 a = b'
65
66 else
67
68 # Check dimensions.
69
70 if ((m = is_square (b)) == 0)
71 error ("lyap: b must be square in a sylvester equation");
47 return; 72 return;
48 endif 73 endif
74
75 [n1,m1] = size(c);
76
77 if (n != n1 || m != m1)
78 error("lyap: a,b,c not conformably dimensioned");
79 endif;
49 endif 80 endif
50 81
51 % set up sylvester equation 82 # Call octave built-in function.
52 c = b;
53 b = a;
54 a = b'
55 else
56 % check dimensions
57 if( (m = is_square(b)) == 0)
58 error("lyap: b must be square in a sylvester equation");
59 return
60 endif
61 [n1,m1] = size(c);
62 if((n ~= n1) || (m ~= m1))
63 error("lyap: a,b,c not conformably dimensioned");
64 endif
65 endif
66 a
67 b
68 c
69 83
70 % call octave built-in function 84 x = syl(a,b,c);
71 x = syl(a,b,c);
72 85
73 disp('LYAP ERR')
74 a*x + x*b + c
75 a=a
76 b=b
77 c=c
78 endfunction 86 endfunction