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is_controllable.m

## Copyright (C) 1993, 1994, 1995, 2000, 2002, 2004, 2005, 2006, 2007
##               Auburn University.  All rights reserved.
##
##
## This program 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.
##
## This program 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 this program; see the file COPYING.  If not, see
## <http://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn {Function File} {[@var{retval}, @var{u}] =} is_controllable (@var{sys}, @var{tol})
## @deftypefnx {Function File} {[@var{retval}, @var{u}] =} is_controllable (@var{a}, @var{b}, @var{tol})
## Logical check for system controllability.
##
## @strong{Inputs}
## @table @var
## @item sys
## system data structure
## @item a
## @itemx b
## @var{n} by @var{n}, @var{n} by @var{m} matrices, respectively
## @item tol
## optional roundoff parameter.  Default value: @code{10*eps}
## @end table
##
## @strong{Outputs}
## @table @var
## @item retval
## Logical flag; returns true (1) if the system @var{sys} or the
## pair (@var{a}, @var{b}) is controllable, whichever was passed as input
## arguments.
## @item u
## @var{u} is an orthogonal basis of the controllable subspace.
## @end table
##
## @strong{Method}
## Controllability is determined by applying Arnoldi iteration with
## complete re-orthogonalization to obtain an orthogonal basis of the
## Krylov subspace
## @example
## span ([b,a*b,...,a^@{n-1@}*b]).
## @end example
## The Arnoldi iteration is executed with @code{krylov} if the system
## has a single input; otherwise a block Arnoldi iteration is performed
## with @code{krylovb}.
## @seealso{size, rows, columns, length, ismatrix, isscalar, isvector, is_observable, is_stabilizable, is_detectable, krylov, krylovb}
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>
## Created: August 1993
## Updated by A. S. Hodel (scotte@eng.auburn.edu) Aubust, 1995 to use krylovb
## Updated by John Ingram (ingraje@eng.auburn.edu) July, 1996 for packed systems

function [retval, U] = is_controllable (a, b, tol)

  deftol = 1;    # assume default tolerance

  if (nargin < 1 || nargin > 3)
    print_usage ();
  elseif (isstruct (a))
    ## system structure passed.
    sys = sysupdate (a, "ss");
    [a, bs] = sys2ss (sys);
    if (nargin > 2)
      print_usage ();
    elseif (nargin == 2)
      tol = b;          % get tolerance
      deftol = 0;
    endif
    b = bs;
  else
    ## a,b arguments sent directly.
    if (nargin < 2)
      print_usage ();
    else
      deftol = 1;
    endif
  endif

  ## check for default tolerance
  if (deftol)
    if (isa (a, "single") || isa (b, "single"))
      tol = 1000 * eps("single");
    else
      tol = 1000*eps;
    endif
  endif

  ## check tol dimensions
  if (! isscalar (tol))
    error ("is_controllable: tol(%dx%d) must be a scalar", ...
           rows (tol), columns (tol));
  elseif (! is_sample (tol))
    error ("is_controllable: tol=%e must be positive",tol);
  endif

  ## check dimensions compatibility
  n = issquare (a);
  [nr, nc] = size (b);

  if (n == 0 || n != nr || nc == 0)
    warning ("is_controllable: a=(%dx%d), b(%dx%d)",rows(a),columns(a),nr,nc);
    retval = 0;
  else
    ## call block-krylov subspace routine to get an orthogonal basis
    ## of the controllable subspace.
    [U, H, Ucols] = krylov (a, b, n, tol, 1);
    retval = (Ucols == n);
  endif

endfunction

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