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dlqe.m
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1999-04-29
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# Copyright (C) 1993, 1994, 1995 John W. Eaton
#
# This file is part of Octave.
#
# Octave 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 2, or (at your option) any
# later version.
#
# Octave 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 Octave; see the file COPYING. If not, write to the Free
# Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
function [l, m, p, e] = dlqe (a, g, c, sigw, sigv, s)
# Usage: [l, m, p, e] = dlqe (A, G, C, SigW, SigV {,S})
#
# Linear quadratic estimator (Kalman filter) design for the
# discrete time system
#
# x[k+1] = A x[k] + B u[k] + G w[k]
# y[k] = C x[k] + D u[k] + w[k]
#
# where w, v are zero-mean gaussian noise processes with respective
# intensities SigW = cov (w, w) and SigV = cov (v, v).
#
# S (if specified) is cov(w,v); otherwise cov(w,v) = 0.
#
# Observer structure is
# z[k+1] = A z[k] + B u[k] + k(y[k] - C z[k] - D u[k]).
#
# Returns:
#
# l = observer gain, (A - L C) is stable
# m = Ricatti equation solution
# p = the estimate error covariance after the measurement update
# e = closed loop poles of (A - L C)
# Written by A. S. Hodel (scotte@eng.auburn.edu) August, 1993.
# Modified for discrete time by R. Bruce Tenison (btenison@eng.auburn.edu)
# October, 1993
if (nargin != 5 && nargin != 6)
error ("dlqe: invalid number of arguments");
endif
# The problem is dual to the regulator design, so transform to dlqr call.
if (nargin == 5)
[k, p, e] = dlqr (a', c', g*sigw*g', sigv);
m = p;
l = k';
else
[k, p, e] = dlqr (a', c', g*sigw*g', sigv, g*s);
m = p;
l = k';
a = a-g*t/sigv*c;
sigw = sigw-t/sigv;
endif
p = a\(m-g*sigw*g')/a';
endfunction