Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / lyap.m

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+## Copyright (C) 2010   Lukas F. Reichlin
+##
+## This file is part of LTI Syncope.
+##
+## LTI Syncope 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 3 of the License, or
+## (at your option) any later version.
+##
+## LTI Syncope 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 LTI Syncope.  If not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn{Function File} {@var{x} =} lyap (@var{a}, @var{b})
+## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{c})
+## @deftypefnx{Function File} {@var{x} =} lyap (@var{a}, @var{b}, @var{[]}, @var{e})
+## Solve continuous-time Lyapunov or Sylvester equations.
+##
+## @strong{Equations}
+## @example
+## @group
+## AX + XA' + B = 0      (Lyapunov Equation)
+##
+## AX + XB + C = 0       (Sylvester Equation)
+##
+## AXE' + EXA' + B = 0   (Generalized Lyapunov Equation)
+## @end group
+## @end example
+##
+## @strong{Algorithm}@*
+## Uses SLICOT SB03MD, SB04MD and SG03AD by courtesy of
+## @uref{http://www.slicot.org, NICONET e.V.}
+##
+## @seealso{lyapchol, dlyap, dlyapchol}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: January 2010
+## Version: 0.2.1
+
+function [x, scale] = lyap (a, b, c, e)
+
+  scale = 1;
+
+  switch (nargin)
+    case 2                                      # Lyapunov equation
+  
+      if (! is_real_square_matrix (a, b))
+        ## error ("lyap: a, b must be real and square");
+        error ("lyap: %s, %s must be real and square", \
+                inputname (1), inputname (2));
+      endif
+  
+      if (rows (a) != rows (b))
+        ## error ("lyap: a, b must have the same number of rows");
+        error ("lyap: %s, %s must have the same number of rows", \
+                inputname (1), inputname (2));
+
+      endif
+
+      [x, scale] = slsb03md (a, -b, false);     # AX + XA' = -B
+
+      ## x /= scale;                            # 0 < scale <= 1
+    
+    case 3                                      # Sylvester equation
+    
+      if (! is_real_square_matrix (a, b))
+        ## error ("lyap: a, b must be real and square");
+        error ("lyap: %s, %s must be real and square", \
+                inputname (1), inputname (2));
+      endif
+
+      if (! is_real_matrix (c) || rows (c) != rows (a) || columns (c) != columns (b))
+        ## error ("lyap: c must be a real (%dx%d) matrix", rows (a), columns (b));
+        error ("lyap: %s must be a real (%dx%d) matrix", \
+                rows (a), columns (b), inputname (3));
+      endif
+
+      x = slsb04md (a, b, -c);  # AX + XB = -C
+
+    case 4                                      # generalized Lyapunov equation
+    
+      if (! isempty (c))
+        print_usage ();
+      endif
+      
+      if (! is_real_square_matrix (a, b, e))
+        ## error ("lyap: a, b, e must be real and square");
+        error ("lyap: %s, %s, %s must be real and square", \
+                inputname (1), inputname (2), inputname (4));
+      endif
+      
+      if (rows (b) != rows (a) || rows (e) != rows (a))
+        ## error ("lyap: a, b, e must have the same number of rows");
+        error ("lyap: %s, %s, %s must have the same number of rows", \
+                inputname (1), inputname (2), inputname (4));
+      endif
+      
+      if (! issymmetric (b))
+        ## error ("lyap: b must be symmetric");
+        error ("lyap: %s must be symmetric", \
+                inputname (2));
+      endif
+
+      [x, scale] = slsg03ad (a, e, -b, false);  # AXE' + EXA' = -B
+      
+      ## x /= scale;                            # 0 < scale <= 1
+
+    otherwise
+      print_usage ();
+
+  endswitch
+
+  if (scale < 1)
+    warning ("lyap: solution scaled by %g to prevent overflow", scale);
+  endif
+
+endfunction
+
+
+## Lyapunov
+%!shared X, X_exp
+%! A = [1, 2; -3, -4];
+%! Q = [3, 1; 1, 1];
+%! X = lyap (A, Q);
+%! X_exp = [ 6.1667, -3.8333;
+%!          -3.8333,  3.0000];
+%!assert (X, X_exp, 1e-4);
+
+## Sylvester
+%!shared X, X_exp
+%! A = [2.0   1.0   3.0
+%!      0.0   2.0   1.0
+%!      6.0   1.0   2.0];
+%!
+%! B = [2.0   1.0
+%!      1.0   6.0];
+%!
+%! C = [2.0   1.0
+%!      1.0   4.0
+%!      0.0   5.0];
+%!
+%! X = lyap (A, B, -C);
+%!
+%! X_exp = [-2.7685   0.5498
+%!          -1.0531   0.6865
+%!           4.5257  -0.4389];
+%!
+%!assert (X, X_exp, 1e-4);
+
+## Generalized Lyapunov
+%!shared X, X_exp
+%! A = [  3.0     1.0     1.0
+%!        1.0     3.0     0.0
+%!        1.0     0.0     2.0];
+%!
+%! E = [  1.0     3.0     0.0
+%!        3.0     2.0     1.0
+%!        1.0     0.0     1.0];
+%!
+%! B = [-64.0   -73.0   -28.0
+%!      -73.0   -70.0   -25.0
+%!      -28.0   -25.0   -18.0];
+%!
+%! X = lyap (A.', -B, [], E.');
+%!
+%! X_exp = [-2.0000  -1.0000   0.0000
+%!          -1.0000  -3.0000  -1.0000
+%!           0.0000  -1.0000  -3.0000];
+%!
+%!assert (X, X_exp, 1e-4);
+