Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/control-2.3.52/obsv.m b/octave_packages/control-2.3.52/obsv.m
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+## Copyright (C) 2009, 2010   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{ob} =} obsv (@var{sys})
+## @deftypefnx {Function File} {@var{ob} =} obsv (@var{a}, @var{c})
+## Return observability matrix.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## LTI model.
+## @item a
+## State transition matrix (n-by-n).
+## @item c
+## Measurement matrix (p-by-n).
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item ob
+## Observability matrix.
+## @end table
+##
+## @strong{Equation}
+## @iftex
+## @tex
+## $$ O_b = \\left[ \\matrix{  C       \\cr
+##                             CA    \\cr
+##                             CA^2  \\cr
+##                             \\vdots  \\cr
+##                             CA^{n-1} } \\right ] $$
+## @end tex
+## @end iftex
+## @ifnottex
+## @example
+## @group
+##      | C        |
+##      | CA       |
+## Ob = | CA^2     |
+##      | ...      |
+##      | CA^(n-1) |
+## @end group
+## @end example
+## @end ifnottex
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: October 2009
+## Version: 0.2
+
+function ob = obsv (a, c)
+
+  if (nargin == 1)           # obsv (sys)
+    ob = ctrb (a.').';       # transpose is overloaded for lti models
+  elseif (nargin == 2)       # obsv (a, c)
+    ob = ctrb (a.', c.').';  # size checked inside
+  else
+    print_usage ();
+  endif
+
+endfunction
+
+
+%!assert (obsv ([1, 0; 0, -0.5], [8, 8]), [8, 8; 8, -4]);