Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / control-2.3.52 / dlqr.m

diff --git a/octave_packages/control-2.3.52/dlqr.m b/octave_packages/control-2.3.52/dlqr.m
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+## Copyright (C) 2009, 2010   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{g}, @var{x}, @var{l}] =} dlqr (@var{sys}, @var{q}, @var{r})
+## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{sys}, @var{q}, @var{r}, @var{s})
+## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r})
+## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s})
+## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{[]}, @var{e})
+## @deftypefnx {Function File} {[@var{g}, @var{x}, @var{l}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{s}, @var{e})
+## Linear-quadratic regulator for discrete-time systems.
+##
+## @strong{Inputs}
+## @table @var
+## @item sys
+## Continuous or discrete-time LTI model (p-by-m, n states).
+## @item a
+## State transition matrix of discrete-time system (n-by-n).
+## @item b
+## Input matrix of discrete-time system (n-by-m).
+## @item q
+## State weighting matrix (n-by-n).
+## @item r
+## Input weighting matrix (m-by-m).
+## @item s
+## Optional cross term matrix (n-by-m).  If @var{s} is not specified, a zero matrix is assumed.
+## @item e
+## Optional descriptor matrix (n-by-n).  If @var{e} is not specified, an identity matrix is assumed.
+## @end table
+##
+## @strong{Outputs}
+## @table @var
+## @item g
+## State feedback matrix (m-by-n).
+## @item x
+## Unique stabilizing solution of the discrete-time Riccati equation (n-by-n).
+## @item l
+## Closed-loop poles (n-by-1).
+## @end table
+##
+## @strong{Equations}
+## @example
+## @group
+## x[k+1] = A x[k] + B u[k],   x[0] = x0
+##
+##         inf
+## J(x0) = SUM (x' Q x  +  u' R u  +  2 x' S u)
+##         k=0
+##
+## L = eig (A - B*G)
+## @end group
+## @end example
+## @seealso{dare, care, lqr}
+## @end deftypefn
+
+## Author: Lukas Reichlin <lukas.reichlin@gmail.com>
+## Created: November 2009
+## Version: 0.2
+
+function [g, x, l] = dlqr (a, b, q, r = [], s = [], e = [])
+
+  if (nargin < 3 || nargin > 6)
+    print_usage ();
+  endif
+
+  if (isa (a, "lti"))
+    s = r;
+    r = q;
+    q = b;
+    [a, b, c, d, e, tsam] = dssdata (a, []);
+  elseif (nargin < 4)
+    print_usage ();
+  else
+    tsam = 1;  # any value > 0 could be used here
+  endif
+
+  if (issample (tsam, -1))
+    [x, l, g] = dare (a, b, q, r, s, e);
+  else
+    [x, l, g] = care (a, b, q, r, s, e);
+  endif
+
+endfunction
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