starp.m

similer program for matlab

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##               Auburn University.  All rights reserved.
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## -*- 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 <[e-mail]>
## 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