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## Copyright (C) 1996, 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} {} starp (@var{P}, @var{K}, @var{ny}, @var{nu})
##
## Redheffer star product or upper/lower LFT, respectively.
## @example
## @group
##
## +-------+
## --------->| |--------->
## | P |
## +--->| |---+ ny
## | +-------+ |
## +-------------------+
## | |
## +----------------+ |
## | |
## | +-------+ |
## +--->| |------+ nu
## | K |
## --------->| |--------->
## +-------+
## @end group
## @end example
## If @var{ny} and @var{nu} ``consume'' all inputs and outputs of
## @var{K} then the result is a lower fractional transformation.
## If @var{ny} and @var{nu} ``consume'' all inputs and outputs of
## @var{P} then the result is an upper fractional transformation.
##
## @var{ny} and/or @var{nu} may be negative (i.e. negative feedback).
## @end deftypefn
## Author: Kai P. Mueller <mueller@ifr.ing.tu-bs.de>
## Created: May 1998
function sys = starp (P, K, ny, nu);
if (nargin != 2 && nargin != 4)
print_usage ();
endif
if (! isstruct (P))
error ("---> P must be in system data structure");
endif
if (! isstruct (K))
error ("---> K must be in system data structure");
endif
P = sysupdate (P, "ss");
[n, nz, mp, pp] = sysdimensions (P);
np = n + nz;
K = sysupdate (K, "ss");
[n, nz, mk, pk] = sysdimensions (K);
nk = n + nz;
ny_sign = 1;
nu_sign = 1;
if (nargin == 2)
## perform a LFT of P and K (upper or lower)
ny = min ([pp, mk]);
nu = min ([pk, mp]);
else
if (ny < 0)
ny = -ny;
ny_sign = -1;
endif
if (nu < 0)
nu = -nu;
nu_sign = -1;
endif
endif
if (ny > pp)
error ("---> P has not enough outputs.");
endif
if (nu > mp)
error ("---> P has not enough inputs.");
endif
if (ny > mk)
error ("---> K has not enough inputs.");
endif
if (nu > pk)
error ("---> K has not enough outputs.");
endif
nwp = mp - nu;
nzp = pp - ny;
nwk = mk - ny;
nzk = pk - nu;
if (nwp + nwk < 1)
error ("---> no inputs left for star product.");
endif
if (nzp + nzk < 1)
error ("---> no outputs left for star product.");
endif
## checks done, form sys
if (nzp)
Olst = 1:nzp;
endif
if (nzk)
Olst = [Olst, pp+nu+1:pp+pk];
endif
if (nwp)
Ilst = 1:nwp;
endif
if (nwk)
Ilst = [Ilst, mp+ny+1:mp+mk];
endif
Clst = zeros (ny+nu, 2);
for ii = 1:nu
Clst(ii,:) = [nwp+ii, nu_sign*(pp+ii)];
endfor
for ii = 1:ny
Clst(nu+ii,:) = [mp+ii, ny_sign*(nzp+ii)];
endfor
sys = buildssic (Clst, [], Olst, Ilst, P, K);
endfunction
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