Mercurial > octave
view scripts/control/dare.m @ 1315:611d403c7f3d
[project @ 1995-06-25 19:56:32 by jwe]
author | jwe |
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date | Sun, 25 Jun 1995 19:56:32 +0000 |
parents | 3f257ab07921 |
children | 52a3f38cbfeb |
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# Copyright (C) 1993, 1994, 1995 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. 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") warning ("dare: opt has an invalid 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) warning ("dare: a,b are not conformable"); endif if (is_controllable (a, b) == 0) warning ("dare: a,b are not controllable"); endif # Check a,c compatibility. if (is_observable (a, c) == 0) 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) warning ("dare: r is not square"); elseif (m1 != m) 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 usage ("x = dare (a, b, c, r {,opt})"); endif endfunction