Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/control-2.3.52/ctrb.m b/octave_packages/control-2.3.52/ctrb.m
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+## Copyright (C) 2009, 2010, 2012   Lukas F. Reichlin
+## Copyright (C) 2009 Luca Favatella <slackydeb@gmail.com>
+##
+## 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{co} =} ctrb (@var{sys})
+## @deftypefnx {Function File} {@var{co} =} ctrb (@var{a}, @var{b})
+## Return controllability matrix.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## LTI model.
+## @item a
+## State transition matrix (n-by-n).
+## @item b
+## Input matrix (n-by-m).
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item co
+## Controllability matrix.
+## @end table
+##
+## @strong{Equation}
+## @iftex
+## @tex
+## $$ C_o = [ B \\ \\ AB \\ \\ A^2B \\ \\ldots \\ A^{n-1}B ] $$
+## @end tex
+## @end iftex
+## @ifnottex
+## @example
+##              2       n-1
+## Co = [ B AB A B ... A   B ]
+## @end example
+## @end ifnottex
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.3
+
+function co = ctrb (a, b)
+
+  if (nargin == 1)       # ctrb (sys)
+    if (! isa (a, "lti"))
+      error ("ctrb: argument must be an lti system");
+    endif
+    [a, b] = ssdata (a);
+  elseif (nargin == 2)   # ctrb (a, b)
+    if (! is_real_square_matrix (a) || ! is_real_matrix (b) || rows (a) != rows (b))
+      error ("ctrb: invalid arguments (a, b)");
+    endif
+  else
+    print_usage ();
+  endif
+
+  n = rows (a);          # number of states
+  k = 0:n-1;             # exponents for a
+
+  tmp = arrayfun (@(x) a^x*b, k, "uniformoutput", false);
+
+  co = horzcat (tmp{:});
+
+endfunction
+
+
+%!assert (ctrb ([1, 0; 0, -0.5], [8; 8]), [8, 8; 8, -4]);