Mercurial > octave-nkf
view scripts/control/are.m @ 77:1cc0af4496c6
[project @ 1993-08-30 15:33:25 by jwe]
author | jwe |
---|---|
date | Mon, 30 Aug 1993 15:33:25 +0000 |
parents | f3c9042fd609 |
children | 16a24e76d6e0 |
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function x = are (a, b, c, opt) # Usage: x = are (a, b, c {,opt}) # # Solves algebraic riccati equation # # a' x + x a - x b x + c = 0 # # for identically dimensioned square matrices a, b, c. If b (c) is not # square, then the function attempts to use b * b' (c' * c) instead. # # Solution method: apply Laub's Schur method (IEEE Trans. Auto. Contr, # 1979) to the appropriate Hamiltonian matrix. # # opt is an option passed to the eigenvalue balancing routine default is "B". # # See also: balance # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. if (nargin == 3 || nargin == 4) if (nargin == 4) if (! (strcmp (opt, "N") || strcmp (opt, "P") ... || strcmp (opt, "S") || strcmp (opt, "B") ... || strcmp (opt, "n") || strcmp (opt, "p") ... || strcmp (opt, "s") || strcmp (opt, "b"))) printf ("warning: are: opt has an illegal value; setting to B"); opt = "B"; endif else opt = "B"; endif if ((n = is_square(a)) == 0) error ("are: a is not square"); endif if (is_controllable(a,b) == 0) printf("warning: are: a, b are not controllable"); endif if ((m = is_square (b)) == 0) b = b * b'; m = rows (b); endif if (is_observable (a, c) == 0) printf ("warning: are: a,c are not observable"); endif if ((p = is_square (c)) == 0) c = c' * c; p = rows (c); endif if (n != m || n != p) error ("are: a, b, c not conformably dimensioned."); endif # Should check for controllability/observability here # use Boley-Golub (Syst. Contr. Letters, 1984) method, not the # # n-1 # rank ([ B A*B ... A^ *B]) method [d, h] = balance ([a, -b; -c, -a'], opt), "A" [u, s] = schur (h, "A"); u = d * u; n1 = n + 1; n2 = 2 * n; x = u (n1:n2, 1:n) / u (1:n, 1:n); else error("usage: x = are (a, b, c)") endif endfunction