Mercurial > octave-nkf
view scripts/control/dare.m @ 74:1b1a6414f9ed
[project @ 1993-08-30 15:07:26 by jwe]
Initial revision
author | jwe |
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date | Mon, 30 Aug 1993 15:07:26 +0000 |
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children | 198c555813f0 |
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function x = dare (a, b, c, r, opt) # Usage: x = dare (a, b, c, r {,opt}) # # Solves discrete-time algebraic riccati equation # # a' x a - x + a' x b (r + b' x b)^{-1} b' x a + c = 0 # # for # # a: nxn # b: nxm # c: nxn, symmetric positive semidefinite # r: mxm, invertible # # If c is not square, then the function attempts to use c'*c instead. # # Solution method: Laub's Schur method (IEEE Trans Auto Contr, 1979) applied # to the appropriate symplectic matrix. # # See also: Ran and Rodman, "Stable Hermitian Solutions of Discrete # Algebraic Riccati Equations," Mathematics of Control, Signals and # Systems, Vol 5, no 2 (1992) pp 165-194. # # opt is an option passed to the eigenvalue balancing routine default # is "B". # # See also: balance, are # Written by A. S. Hodel (scotte@eng.auburn.edu) August 1993. if (nargin == 4 || nargin == 5) if (nargin == 5) if (opt != "N" || opt != "P" || opt != "S" || opt != "B") fprintf (stderr, "dare: opt has an illegal value -- setting to B"); opt = "B"; endif else opt = "B"; endif # Check a matrix dimensions if ((n = is_square (a)) == 0) error ("dare: a is not square"); endif # Check a,b compatibility. [n1, m] = size (b); if (n1 != n) fprintf (stderr, "warning: dare: a,b are not conformable"); endif if (is_controllable (a, b) == 0) fprintf ("warning: dare: a,b are not controllable"); endif # Check a,c compatibility. if (is_observable (a, c) == 0) fprintf (stderr "warning: dare: a,c are not observable"); endif if ((p = is_square (c)) == 0) c = c'*c; p = rows (c); endif if (n != p) error ("dare: a,c are not conformable"); endif # Check r dimensions. if ((m1 = is_square (r)) == 0) fprintf("warning: dare: r is not square"); elseif (m1 != m) fprintf(stderr, "warning: b,r are not conformable"); endif brb = (b/r)*b'; atc = a'\c; [d, sy] = balance ([a + brb*atc, -brb/(a'); -atc, inv (a')], opt); [u, s] = schur(sy,'D'); u = d*u; n1 = n+1; n2 = 2*n; x = u (n1:n2, 1:n)/u(1:n, 1:n); else error ("usage: x = dare (a, b, c, r {,opt})"); endif endfunction