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ss.m

## Copyright (C) 1996, 1998, 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{outsys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @var{n}, @var{nz}, @var{stname}, @var{inname}, @var{outname}, @var{outlist})
## Create system structure from state-space data.   May be continuous,
## discrete, or mixed (sampled data)
##
## @strong{Inputs}
## @table @var
## @item a
## @itemx b
## @itemx c
## @itemx d
## usual state space matrices.
##
## default: @var{d} = zero matrix
##
## @item   tsam
## sampling rate.  Default: @math{tsam = 0} (continuous system)
##
## @item n
## @itemx nz
## number of continuous, discrete states in the system
##
## If @var{tsam} is 0, @math{n = @code{rows}(@var{a})}, @math{nz = 0}.
##
## If @var{tsam} is greater than zero, @math{n = 0},
## @math{nz = @code{rows}(@var{a})}
##
## see below for system partitioning
##
## @item  stname
## cell array of strings of state signal names
##
## default (@var{stname}=[] on input): @code{x_n} for continuous states,
##                     @code{xd_n} for discrete states
##
## @item inname
## cell array of strings of input signal names
##
## default (@var{inname} = [] on input): @code{u_n}
##
## @item outname
## cell array of strings of output signal names
##
## default (@var{outname} = [] on input): @code{y_n}
##
## @item   outlist
##
## list of indices of outputs y that are sampled
##
## If @var{tsam} is 0, @math{outlist = []}.
##
## If @var{tsam} is greater than 0, @math{outlist = 1:@code{rows}(@var{c})}.
## @end table
##
## Unlike states, discrete/continuous outputs may appear in any order.
##
## @code{sys2ss} returns a vector @var{yd} where
## @var{yd}(@var{outlist}) = 1; all other entries of @var{yd} are 0.
##
## @strong{Output}
## @table @var
## @item outsys
## system data structure
## @end table
##
## @strong{System partitioning}
##
## Suppose for simplicity that outlist specified
## that the first several outputs were continuous and the remaining outputs
## were discrete.  Then the system is partitioned as
## @example
## @group
## x = [ xc ]  (n x 1)
##     [ xd ]  (nz x 1 discrete states)
## a = [ acc acd ]  b = [ bc ]
##     [ adc add ]      [ bd ]
## c = [ ccc ccd ]  d = [ dc ]
##     [ cdc cdd ]      [ dd ]
##
##     (cdc = c(outlist,1:n), etc.)
## @end group
## @end example
## with dynamic equations:
## @ifinfo
## @math{d/dt xc(t)     = acc*xc(t)      + acd*xd(k*tsam) + bc*u(t)}
##
## @math{xd((k+1)*tsam) = adc*xc(k*tsam) + add*xd(k*tsam) + bd*u(k*tsam)}
##
## @math{yc(t)      = ccc*xc(t)      + ccd*xd(k*tsam) + dc*u(t)}
##
## @math{yd(k*tsam) = cdc*xc(k*tsam) + cdd*xd(k*tsam) + dd*u(k*tsam)}
## @end ifinfo
## @iftex
## @tex
## $$\eqalign{
## {d \over dt} x_c(t)
##   & =   a_{cc} x_c(t)      + a_{cd} x_d(k*t_{sam}) + bc*u(t) \cr
## x_d((k+1)*t_{sam})
##   & =   a_{dc} x_c(k t_{sam}) + a_{dd} x_d(k t_{sam}) + b_d u(k t_{sam}) \cr
## y_c(t)
##  & =  c_{cc} x_c(t) + c_{cd} x_d(k t_{sam}) + d_c u(t) \cr
## y_d(k t_{sam})
##   & =  c_{dc} x_c(k t_{sam}) + c_{dd} x_d(k t_{sam}) + d_d u(k t_{sam})
## }$$
## @end tex
## @end iftex
##
## @strong{Signal partitions}
## @example
## @group
##         | continuous      | discrete               |
## ----------------------------------------------------
## states  | stname(1:n,:)   | stname((n+1):(n+nz),:) |
## ----------------------------------------------------
## outputs | outname(cout,:) | outname(outlist,:)     |
## ----------------------------------------------------
## @end group
## @end example
## where @math{cout} is the list of in 1:@code{rows}(@var{p})
## that are not contained in outlist. (Discrete/continuous outputs
## may be entered in any order desired by the user.)
##
## @strong{Example}
## @example
## octave:1> a = [1 2 3; 4 5 6; 7 8 10];
## octave:2> b = [0 0 ; 0 1 ; 1 0];
## octave:3> c = eye (3);
## octave:4> sys = ss (a, b, c, [], 0, 3, 0, ...
## >                   @{"volts", "amps", "joules"@});
## octave:5> sysout(sys);
## Input(s)
##         1: u_1
##         2: u_2
##
## Output(s):
##         1: y_1
##         2: y_2
##         3: y_3
##
## state-space form:
## 3 continuous states, 0 discrete states
## State(s):
##         1: volts
##         2: amps
##         3: joules
##
## A matrix: 3 x 3
##    1   2   3
##    4   5   6
##    7   8  10
## B matrix: 3 x 2
##   0  0
##   0  1
##   1  0
## C matrix: 3 x 3
##   1  0  0
##   0  1  0
##   0  0  1
## D matrix: 3 x 3
##   0  0
##   0  0
##   0  0
## @end example
## Notice that the @math{D} matrix is constructed  by default to the
## correct dimensions.  Default input and output signals names were assigned
## since none were given.
## @end deftypefn

## Author: John Ingram <ingraje@eng.auburn.edu>
## Created: July 20, 1996

function retsys = ss (a, b, c, d, tsam, n, nz, stname, inname, outname, outlist)

  ## Test for correct number of inputs
  if (nargin < 3 || nargin > 11)
    print_usage ();
  endif

  ## verify A, B, C, D arguments
  ## If D is not specified, set it to a zero matrix of appriate dimension.
  if (nargin == 3)
    d = zeros (rows (c), columns (b));
  elseif (isempty (d))
    d = zeros (rows (c), columns (b));
  endif

  ## Check the dimensions
  [na, m, p] = abcddim (a, b, c, d);

  ## If dimensions are wrong, exit function
  if (m == -1)
    error ("a(%dx%d), b(%dx%d), c(%dx%d), d(%dx%d); incompatible",
         rows (a), columns (a), rows (b), columns (b),
         rows (c), columns (c), rows (d), columns (d));
  endif

  ## check for tsam input
  if (nargin < 5)
    tsam = 0;
  elseif (! (is_sample (tsam) || tsam == 0))
    error ("tsam must be a nonnegative real scalar");
  endif

  ## check for continuous states
  if (nargin < 6 && tsam == 0)
    n = na;
  elseif (nargin < 6)
    n = 0;
  elseif (! ismatrix (n) || ischar (n))
    error ("Parameter n is not a numerical value.");
  elseif (! isscalar(n) || n < 0 || n != round (n))
    if (isscalar (n))
      error ("invalid value of n=%d,%e", n, n);
    else
      error ("invalid value of n=(%dx%d)", rows (n), columns (n));
    endif
  endif

  ## check for num discrete states
  if (nargin < 7 && tsam == 0)
    nz = 0;
  elseif (nargin < 7)
    nz = na - n;
  elseif (! ismatrix(nz) || ischar (nz))
    error ("Parameter nz is not a numerical value.");
  elseif (! isscalar(nz) || nz < 0 || nz != round(nz))
    if (isscalar (nz))
      error ("invalid value of nz=%d", nz);
    else
      error ("invalid value of nz=(%d,%d)", rows (nz), columns (nz));
    endif
  endif

  ## check for total number of states
  if ((n + nz) != na)
    error ("invalid: a is %dx%d, n=%d, nz=%d", na, na, n, nz);
  endif

  ## construct system with default names
  retsys.a = a;
  retsys.b = b;
  retsys.c = c;
  retsys.d = d;

  retsys.n = n;
  retsys.nz = nz;
  retsys.tsam = tsam;
  retsys.yd = zeros (1, p);     # default value entered below

  ## Set the system vector:  active = 2(ss), updated = [0 0 1];
  retsys.sys = ;

  retsys.stname = __sysdefstname__ (n, nz);
  retsys.inname = __sysdefioname__ (m, "u");
  retsys.outname = __sysdefioname__ (p, "y");

  ## check for state names
  if (nargin >= 8)
    if (! isempty (stname))
      retsys = syssetsignals (retsys, "st", stname);
    endif
  endif

  ## check for input names
  if (nargin >= 9)
    if (! isempty (inname))
      retsys = syssetsignals (retsys, "in", inname);
    endif
  endif

  ## check for output names
  if (nargin >= 10)
    if (! isempty (outname))
      retsys = syssetsignals (retsys, "out", outname);
    endif
  endif

  ## set up yd
  if (nargin < 11)
    retsys = syssetsignals (retsys, "yd", ones(1,p)*(tsam > 0));
  else
    if (! isempty (outlist))
      retsys = syssetsignals (retsys, "yd", ones (size (outlist)), outlist);
    endif
  endif

endfunction

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