# HG changeset patch
# User jwe
# Date 746723246 0
# Node ID 1b1a6414f9ed1368987a3c91d4f7fbfc25a95417
# Parent  f3c9042fd6094954b10b91f677f584d84c503d53
[project @ 1993-08-30 15:07:26 by jwe]
Initial revision

diff -r f3c9042fd609 -r 1b1a6414f9ed scripts/control/dare.m
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/control/dare.m	Mon Aug 30 15:07:26 1993 +0000
@@ -0,0 +1,94 @@
+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