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## 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 <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{p} =} pole (@var{sys})
## Compute poles of @acronym{LTI} system.
##
## @strong{Inputs}
## @table @var
## @item sys
## @acronym{LTI} model.
## @end table
##
## @strong{Outputs}
## @table @var
## @item p
## Poles of @var{sys}.
## @end table
##
## @strong{Algorithm}@*
## For (descriptor) state-space models and system/state matrices, @command{pole}
## relies on Octave's @command{eig}.
## For @acronym{SISO} transfer functions, @command{pole}
## uses Octave's @command{roots}.
## @acronym{MIMO} transfer functions are converted to
## a @emph{minimal} state-space representation for the
## computation of the poles.
##
## @end deftypefn
## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
## Contributor: Mark Bronsfeld <m.brnsfld@googlemail.com>
## Created: October 2009
## Version: 0.2
function pol = pole (sys)
if(nargin == 1) # pole(sys)
if(!(isa(sys, "lti")) && issquare(sys))
pol = eig(sys);
elseif(isa(sys, "lti"))
pol = __pole__(sys);
else
error("pole: argument must be an LTI system");
endif
else
print_usage();
endif
endfunction
%!shared pol_exp, pol_obs
%! A = [-1, 0, 0;
%! 0, -2, 0;
%! 0, 0, -3];
%! pol_exp = [-3;
%! -2;
%! -1];
%! pol_obs = pole(A);
%!assert(pol_obs, pol_exp, 0);
## Poles of descriptor state-space model
%!shared pol, pol_exp, infp, kronr, kronl, infp_exp, kronr_exp, kronl_exp
%! A = [ 1 0 0 0 0 0 0 0 0
%! 0 1 0 0 0 0 0 0 0
%! 0 0 1 0 0 0 0 0 0
%! 0 0 0 1 0 0 0 0 0
%! 0 0 0 0 1 0 0 0 0
%! 0 0 0 0 0 1 0 0 0
%! 0 0 0 0 0 0 1 0 0
%! 0 0 0 0 0 0 0 1 0
%! 0 0 0 0 0 0 0 0 1 ];
%!
%! E = [ 0 0 0 0 0 0 0 0 0
%! 1 0 0 0 0 0 0 0 0
%! 0 1 0 0 0 0 0 0 0
%! 0 0 0 0 0 0 0 0 0
%! 0 0 0 1 0 0 0 0 0
%! 0 0 0 0 1 0 0 0 0
%! 0 0 0 0 0 0 0 0 0
%! 0 0 0 0 0 0 1 0 0
%! 0 0 0 0 0 0 0 1 0 ];
%!
%! B = [ -1 0 0
%! 0 0 0
%! 0 0 0
%! 0 -1 0
%! 0 0 0
%! 0 0 0
%! 0 0 -1
%! 0 0 0
%! 0 0 0 ];
%!
%! C = [ 0 1 1 0 3 4 0 0 2
%! 0 1 0 0 4 0 0 2 0
%! 0 0 1 0 -1 4 0 -2 2 ];
%!
%! D = [ 1 2 -2
%! 0 -1 -2
%! 0 0 0 ];
%!
%! sys = dss (A, B, C, D, E, "scaled", true);
%! [pol, ~, infp, kronr, kronl] = __sl_ag08bd__ (A, E, [], [], [], true);
%!
%! pol_exp = zeros (0,1);
%!
%! infp_exp = [0, 3];
%! kronr_exp = zeros (1,0);
%! kronl_exp = zeros (1,0);
%!
%!assert (pol, pol_exp, 1e-4);
%!assert (infp, infp_exp);
%!assert (kronr, kronr_exp);
%!assert (kronl, kronl_exp);
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