lqg

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{k}, @var{q1}, @var{p1}, @var{ee}, @var{er}] =} lqg (@var{sys}, @var{sigw}, @var{sigv}, @var{q}, @var{r}, @var{in_idx})
% Design a linear-quadratic-gaussian optimal controller for the system
% @example
% dx/dt = A x + B u + G w       [w]=N(0,[Sigw 0    ])
%     y = C x + v               [v]  (    0   Sigv ])
% @end example
% or
% @example
% x(k+1) = A x(k) + B u(k) + G w(k)   [w]=N(0,[Sigw 0    ])
%   y(k) = C x(k) + v(k)              [v]  (    0   Sigv ])
% @end example
%
% @strong{Inputs}
% @table @var
% @item  sys
% system data structure
% @item  sigw
% @itemx  sigv
% intensities of independent Gaussian noise processes (as above)
% @item  q
% @itemx  r
% state, control weighting respectively.  Control @acronym{ARE} is
% @item  in_idx
% names or indices of controlled inputs (see @command{sysidx}, @command{cellidx})
%
% default: last dim(R) inputs are assumed to be controlled inputs, all
% others are assumed to be noise inputs.
% @end table
% @strong{Outputs}
% @table @var
% @item    k
% system data structure format @acronym{LQG} optimal controller (Obtain A, B, C
% matrices with @command{sys2ss}, @command{sys2tf}, or @command{sys2zp} as
% appropriate).
% @item    p1
% Solution of control (state feedback) algebraic Riccati equation.
% @item    q1
% Solution of estimation algebraic Riccati equation.
% @item    ee
% Estimator poles.
% @item    es
% Controller poles.
% @end table
% @seealso{h2syn, lqe, lqr}
% @end deftypefn