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sysmin.m

## Copyright (C) 1996, 2000, 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{retsys}, @var{nc}, @var{no}] =} sysmin (@var{sys}, @var{flg})
## Returns a minimal (or reduced order) system
##
## @strong{Inputs}
## @table @var
## @item sys
## System data structure
## @item flg
## When equal to 0 (default value), returns minimal system,
## in which state names are lost; when equal to 1, returns system 
## with physical states removed that are either uncontrollable or 
## unobservable (cannot reduce further without discarding physical
## meaning of states).
## @end table
## @strong{Outputs}
## @table @var
## @item retsys
## Returned system.
## @item nc
## Number of controllable states in the returned system.
## @item no
## Number of observable states in the returned system.
## @item cflg
## @code{is_controllable(retsys)}.
## @item oflg
## @code{is_observable(retsys)}.
## @end table
## @end deftypefn

## Author: A. S. Hodel <a.s.hodel@eng.auburn.edu>

function [retsys, nc, no, cflg, oflg] = sysmin (sys, flg)

  switch (nargin)
  case 1
    flg = 0;
  case 2
    jnk = flg;    # dummy operation
  otherwise,
    print_usage ();
  endswitch

  dflg = is_digital (sys, 2);

  [n, nz, m, p] = sysdimensions (sys);

  if (n*nz > 0)
    # both continuous and discrete states
    [aa, bb, cc, dd, tsam, n, nz, stnam, innam, outnam, yd] = sys2ss (sys);
    crng = 1:n;
    drng = n+(1:nz);

    # get minimal realization of continuous part
    Ac  = aa(crng,crng);
    Acd = aa(crng,drng);
    Adc = aa(drng,crng);
    Ad  = aa(drng,drng);
    Bc  = bb(crng,:);
    Bd  = bb(drng,:);
    Cc  = cc(:,crng);
    Cd  = cc(:,drng);

    cstnam = stnam(crng);
    dstnam = stnam(drng);
    cinnam = __sysconcat__ (innam, stnam(drng));
    coutnam = __sysconcat__ (outnam, stnam(drng));
    csys = ss (Ac, [Bc, Acd], [Cc; Adc]);
    csys = syssetsignals (csys, "st", cstnam);
    csys = syssetsignals (csys, "in", cinnam);
    csys = syssetsignals (csys, "out", coutnam);

    # reduce continuous system, recombine with discrete part
    csys = sysmin (csys, flg);
    cn = sysdimensions (csys);

    if (cn == 0)
      # continuous states are removed; just reduce the discrete part
      sys = sysprune (sys, 1:p, 1:m, drng);
      retsys = sysmin (sys, flg);
    else
      # extract updated parameters from reduced continuous system
      [caa, cbb, ccc, cdd, ctsam, cn, cnz, cstnam, cinnam, coutnam] ...
        = sys2ss (csys);

      crng = 1:cn;
      Ac  = caa;
      Bc  = cbb(:,1:m);
      Acd = cbb(:,m+(1:nz));
      Cc  = ccc(1:p,:);
      Adc = ccc(p + (1:nz),:);

      # recombine to reduce discrete part of the system
      dinnam = __sysconcat__ (innam, cstnam);
      doutnam = __sysconcat__ (outnam, cstnam);
      dsys = ss (Ad, [Bd, Adc], [Cd; Acd], , tsam);
      dsys = syssetsignals (dsys, "st", dstnam);
      dsys = syssetsignals (dsys, "in", dinnam);
      dsys = syssetsignals (dsys, "out", doutnam);

      # reduce discrete subsystem
      dsys = sysmin (dsys);
      [n1, nz] = sysdimensions (dsys);
      if (nz == 0)
        # discrete subsystem is not needed
        retsys = sysprune (csys, 1:p, 1:m);
      else
        # combine discrete, continuous subsystems
        [Ad, dbb, dcc] = sys2ss (dsys);
        dstnam = sysgetsignals (dsys, "st");
        Bd  = dbb(:,1:m);
        Adc = dbb(:,m+(1:cn));
        Cd  = dcc(1:p,:);
        Acd = dcc(p+(1:cn),:);
        stnam = __sysconcat__ (cstnam, dstnam);
        aa = [Ac, Acd; Adc, Ad];
        bb = [Bc; Bd];
        cc = [Cc, Cd];
        retsys = ss ([Ac, Acd; Adc, Ad], [Bc ; Bd], [Cc, Cd], dd, tsam,
                 cn, nz, stnam, innam, outnam, find(yd == 1));
      endif
    endif
  else
    Ts = sysgettsam (sys);
    switch (flg)
    case 0
      ## reduce to a minimal system
      [aa, bb, cc, dd] = sys2ss (sys);
      [cflg, Uc] = is_controllable (aa, bb);
      if (! cflg)
        ## reduce to controllable states
        if (! isempty (Uc))
          aa = Uc'*aa*Uc;
          bb = Uc'*bb;
          cc = cc*Uc;
        else
          aa = bb = cc = ;
        endif
      endif
      if (! isempty (aa))
        [oflg, Uo] = is_observable (aa, cc);
        if (! oflg)
          if (! isempty (Uo))
            aa = Uo'*aa*Uo;
            bb = Uo'*bb;
            cc = cc*Uo;
          else
            aa = bb = cc = ;
          endif
        endif
      endif
      switch (dflg)
      case 0
        nc = no = nn = columns (aa);
        nz = 0;
      case 1
        nc = no = nz = columns (aa);
        nn = 0;
      endswitch
      innam = sysgetsignals (sys, "in");
      outnam= sysgetsignals (sys, "out");
      retsys = ss (aa, bb, cc, dd, Ts, nn, nz, [], innam, outnam);
    case 1
      ## reduced model with physical states
      [cflg, Uc] = is_controllable (sys);
      xc = find (max (abs (Uc')) != 0);
      [oflg, Uo] = is_observable (sys);
      xo = find (max (abs (Uo')) != 0);
      xx = intersection (xc, xo);
      ## signal no states in reduced model
      if (isempty (xx))
      xx = 0;
      endif
      retsys = sysprune (sys, [], [], xx);
    otherwise
      error ("invalid value of flg = %d", flg);
    endswitch
    if (sysdimensions (retsys, "st") > 0)
      [cflg, Uc] = is_controllable (retsys);
      nc = columns (Uc);
      [oflg, Uo] = is_observable (retsys);
      no = columns (Uo);
    else
      nc = no = 0;
    endif
  endif

endfunction

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