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lqe

PURPOSE ^

% Construct the linear quadratic estimator (Kalman filter) for the

SYNOPSIS ^

function [k, p, e] = lqe (a, g, c, sigw, sigv, zz)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{k}, @var{p}, @var{e}] =} lqe (@var{a}, @var{g}, @var{c}, @var{sigw}, @var{sigv}, @var{z})
% Construct the linear quadratic estimator (Kalman filter) for the
% continuous time system
% @iftex
% @tex
% $$
%  {dx\over dt} = A x + G u
% $$
% $$
%  y = C x + v
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% dx
% -- = A x + G u
% dt
%
% y = C x + v
% @end example
%
% @end ifinfo
% where @var{w} and @var{v} are zero-mean gaussian noise processes with
% respective intensities
%
% @example
% sigw = cov (w, w)
% sigv = cov (v, v)
% @end example
%
% The optional argument @var{z} is the cross-covariance
% @code{cov (@var{w}, @var{v})}.  If it is omitted,
% @code{cov (@var{w}, @var{v}) = 0} is assumed.
%
% Observer structure is @code{dz/dt = A z + B u + k (y - C z - D u)}
%
% The following values are returned:
%
% @table @var
% @item k
% The observer gain,
% @iftex
% @tex
% $(A - K C)$
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{k}@var{c})
% @end ifinfo
% is stable.
%
% @item p
% The solution of algebraic Riccati equation.
%
% @item e
% The vector of closed loop poles of
% @iftex
% @tex
% $(A - K C)$.
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{k}@var{c}).
% @end ifinfo
% @end table
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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