## Copyright (C) 2009-2016 Lukas F. Reichlin
##
## This file is part of LTI Syncope.
##
## LTI Syncope 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.
##
## LTI Syncope 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 LTI Syncope. If not, see .
## -*- texinfo -*-
## @deftypefn {Function File} {@var{sys} =} ss (@var{sys})
## @deftypefnx {Function File} {@var{sys} =} ss (@var{d}, @dots{})
## @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @dots{})
## @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c}, @dots{})
## @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @dots{})
## @deftypefnx {Function File} {@var{sys} =} ss (@var{a}, @var{b}, @var{c}, @var{d}, @var{tsam}, @dots{})
## Create or convert to state-space model.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model to be converted to state-space.
## @item a
## State matrix (n-by-n).
## @item b
## Input matrix (n-by-m).
## @item c
## Output matrix (p-by-n).
## If @var{c} is empty @code{[]} or not specified, an identity matrix is assumed.
## @item d
## Feedthrough matrix (p-by-m).
## If @var{d} is empty @code{[]} or not specified, a zero matrix is assumed.
## @item tsam
## Sampling time in seconds. If @var{tsam} is not specified, a continuous-time model is assumed.
## @item @dots{}
## Optional pairs of properties and values.
## Type @command{set (ss)} for more information.
## @end table
##
## @strong{Outputs}
## @table @var
## @item sys
## State-space model.
## @end table
##
## @strong{Option Keys and Values}
## @table @var
## @item 'a', 'b', 'c', 'd', 'e'
## State-space matrices. See 'Inputs' for details.
##
## @item 'stname'
## The name of the states in @var{sys}.
## Cell vector containing strings for each state.
## Default names are @code{@{'x1', 'x2', ...@}}
##
## @item 'scaled'
## Logical. If set to true, no automatic scaling is used,
## e.g. for frequency response plots.
##
## @item 'tsam'
## Sampling time. See 'Inputs' for details.
##
## @item 'inname'
## The name of the input channels in @var{sys}.
## Cell vector of length m containing strings.
## Default names are @code{@{'u1', 'u2', ...@}}
##
## @item 'outname'
## The name of the output channels in @var{sys}.
## Cell vector of length p containing strings.
## Default names are @code{@{'y1', 'y2', ...@}}
##
## @item 'ingroup'
## Struct with input group names as field names and
## vectors of input indices as field values.
## Default is an empty struct.
##
## @item 'outgroup'
## Struct with output group names as field names and
## vectors of output indices as field values.
## Default is an empty struct.
##
## @item 'name'
## String containing the name of the model.
##
## @item 'notes'
## String or cell of string containing comments.
##
## @item 'userdata'
## Any data type.
## @end table
##
## @strong{Equations}
## @example
## @group
## .
## x = A x + B u
## y = C x + D u
## @end group
## @end example
##
## @strong{Example}
## @example
## @group
## octave:1> a = [1 2 3; 4 5 6; 7 8 9];
## octave:2> b = [10; 11; 12];
## octave:3> stname = @{'V', 'A', 'kJ'@};
## octave:4> sys = ss (a, b, 'stname', stname)
## @end group
## @end example
##
## @example
## @group
## sys.a =
## V A kJ
## V 1 2 3
## A 4 5 6
## kJ 7 8 9
## @end group
## @end example
##
## @example
## @group
## sys.b =
## u1
## V 10
## A 11
## kJ 12
## @end group
## @end example
##
## @example
## @group
## sys.c =
## V A kJ
## y1 1 0 0
## y2 0 1 0
## y3 0 0 1
## @end group
## @end example
##
## @example
## @group
## sys.d =
## u1
## y1 0
## y2 0
## y3 0
##
## Continuous-time model.
## octave:5>
## @end group
## @end example
##
## @strong{Note on compatibility}
##
## If the state-space model @var{sys} is converted from a transfer
## function, the resulting state-space model can be transformed into
## the form computed by Matlab (a controllable canonical form with
## flipped state variables order) by using the following
## similarity transformation:
##
## @example
## @group
## n = size (sys.a, 1)
## QSi = inv (ctrb (sys))
## T(n,:) = QSi(n,:)
## for i=n-1:-1:1, T(i,:) = T(i+1,:)*sys.a, endfor
## sys_ml = ss2ss (sys, T)
## @end group
## @end example
##
## @seealso{tf, dss}
## @end deftypefn
## Author: Lukas Reichlin
## Created: September 2009
## Version: 0.4
function sys = ss (varargin)
## model precedence: frd > ss > zpk > tf > double
## inferiorto ("frd");
superiorto ("zpk", "tf", "double");
if (nargin == 1) # shortcut for lti objects
if (isa (varargin{1}, "ss")) # already in ss form sys = ss (sssys)
sys = varargin{1};
return;
elseif (isa (varargin{1}, "lti")) # another lti object sys = ss (sys)
[sys, lti] = __sys2ss__ (varargin{1});
sys.lti = lti; # preserve lti properties
return;
endif
elseif (nargin == 2) # shortcut for lti objects plus
if (ischar (varargin{2}) && isa (varargin{1}, "lti"))
candidates = {"minimal", "explicit"};
key = __match_key__ (varargin{2}, candidates, "ss");
switch (key)
case "minimal" # ss (sys, 'minimal')
sys = minreal (ss (varargin{1}));
return;
case "explicit" # ss (sys, 'explicit')
sys = dss2ss (ss (varargin{1}));
return;
otherwise # this would be a silly bug
endswitch
endif
endif
a = []; b = []; c = []; d = []; # default state-space matrices
tsam = 0; # default sampling time
[mat_idx, opt_idx, obj_flg] = __lti_input_idx__ (varargin);
switch (numel (mat_idx))
case 1
d = varargin{mat_idx};
case 2
[a, b] = varargin{mat_idx};
case 3
[a, b, c] = varargin{mat_idx};
case 4
[a, b, c, d] = varargin{mat_idx};
case 5
[a, b, c, d, tsam] = varargin{mat_idx};
if (isempty (tsam) && is_real_matrix (tsam))
tsam = -1;
elseif (! issample (tsam, -10))
error ("ss: invalid sampling time");
endif
case 0
## nothing to do here, just prevent case 'otherwise'
otherwise
print_usage ();
endswitch
varargin = varargin(opt_idx);
if (obj_flg)
varargin = horzcat ({"lti"}, varargin);
endif
[a, b, c, d, tsam] = __adjust_ss_data__ (a, b, c, d, tsam);
[p, m, n] = __ss_dim__ (a, b, c, d); # determine number of outputs, inputs and states
stname = repmat ({""}, n, 1); # cell with empty state names
ssdata = struct ("a", a, "b", b,
"c", c, "d", d,
"e", [],
"stname", {stname},
"scaled", false); # struct for ss-specific data
ltisys = lti (p, m, tsam); # parent class for general lti data
sys = class (ssdata, "ss", ltisys); # create ss object
if (numel (varargin) > 0) # if there are any properties and values, ...
sys = set (sys, varargin{:}); # use the general set function
endif
endfunction
## TODO: create a separate function @lti/dss2ss.m
function G = dss2ss (G)
[G.a, G.b, G.c, G.d, G.e] = __dss2ss__ (G.a, G.b, G.c, G.d, G.e);
endfunction