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tf2ss.m

## Copyright (C) 1996, 1998, 2000, 2002, 2004, 2005, 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{a}, @var{b}, @var{c}, @var{d}] =} tf2ss (@var{num}, @var{den})
## Conversion from transfer function to state-space.
## The state space system:
## @iftex
## @tex
## $$ \dot x = Ax + Bu $$
## $$ y = Cx + Du $$
## @end tex
## @end iftex
## @ifinfo
## @example
##       .
##       x = Ax + Bu
##       y = Cx + Du
## @end example
## @end ifinfo
## is obtained from a transfer function:
## @iftex
## @tex
## $$ G(s) = { { \rm num }(s) \over { \rm den }(s) } $$
## @end tex
## @end iftex
## @ifinfo
## @example
##                 num(s)
##           G(s)=-------
##                 den(s)
## @end example
## @end ifinfo
##
## The vector @var{den} must contain only one row, whereas the vector 
## @var{num} may contain as many rows as there are outputs @var{y} of 
## the system. The state space system matrices obtained from this function 
## will be in controllable canonical form as described in @cite{Modern Control 
## Theory}, (Brogan, 1991).
## @end deftypefn

## Author: R. Bruce Tenison <btenison@eng.auburn.edu>
## Created: June 22, 1994
## mod A S Hodel July, Aug  1995

function [a, b, c, d] = tf2ss (num, den)

  if (nargin != 2)
    print_usage ();
  elseif (isempty (num))
    error ("tf2ss: empty numerator");
  elseif (isempty (den))
    error ("tf2ss: empy denominator");
  elseif (! isvector (num))
    error ("num(%dx%d) must be a vector", rows (num), columns (num));
  elseif (! isvector (den))
    error ("den(%dx%d) must be a vector", rows (den), columns (den));
  endif

  ## strip leading zeros from num, den
  nz = find (num != 0);
  if (isempty (nz))
    num = 0;
  else
    num = num(nz(1):length(num));
  endif
  nz = find (den != 0);
  if (isempty (nz))
    error ("denominator is 0.");
  else
    den = den(nz(1):length(den));
  endif

  ## force num, den to be row vectors
  num = vec (num)';
  den = vec (den)';
  nn = length (num);
  nd = length (den);
  if (nn > nd)
    error ("deg(num)=%d > deg(den)= %d", nn, nd);
  endif

   ## Check sizes
   if (nd == 1)
     a = b = c = ;
     d = num(:,1) / den(1);
   else
    ## Pad num so that length(num) = length(den)
    if (nd-nn > 0)
      num = [zeros(1,nd-nn), num];
    endif

    ## Normalize the numerator and denominator vector w.r.t. the leading
    ## coefficient
    d1 = den(1);
    num = num / d1;
    den = den(2:nd)/d1;
    sw = nd-1:-1:1;

    ## Form the A matrix
    if (nd > 2)
      a = ;
    else
      a = -den(sw);
    endif

    ## Form the B matrix
    b = zeros (nd-1, 1);
    b(nd-1,1) = 1;

    ## Form the C matrix
    c = num(:,2:nd)-num(:,1)*den;
    c = c(:,sw);

    ## Form the D matrix
    d = num(:,1);
  endif

endfunction

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