## Copyright (C) 1993, 1994, 1995, 2000, 2002, 2004, 2005, 2006, 2007
##               Auburn University.  All rights reserved.
##
## This file is part of Octave.
##
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## 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.
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## General Public License for more details.
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## -*- 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) tol = 1000*eps; 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