dlqr

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{k}, @var{p}, @var{e}] =} dlqr (@var{a}, @var{b}, @var{q}, @var{r}, @var{z})
% Construct the linear quadratic regulator for the discrete time system
% @iftex
% @tex
% $$
%  x_{k+1} = A x_k + B u_k
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% x[k+1] = A x[k] + B u[k]
% @end example
%
% @end ifinfo
% to minimize the cost functional
% @iftex
% @tex
% $$
%  J = \sum x^T Q x + u^T R u
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% J = Sum (x' Q x + u' R u)
% @end example
% @end ifinfo
%
% @noindent
% @var{z} omitted or
% @iftex
% @tex
% $$
%  J = \sum x^T Q x + u^T R u + 2 x^T Z u
% $$
% @end tex
% @end iftex
% @ifinfo
%
% @example
% J = Sum (x' Q x + u' R u + 2 x' Z u)
% @end example
%
% @end ifinfo
% @var{z} included.
%
% The following values are returned:
%
% @table @var
% @item k
% The state feedback gain,
% @iftex
% @tex
% $(A - B K)$
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{b}@var{k})
% @end ifinfo
% is stable.
%
% @item p
% The solution of algebraic Riccati equation.
%
% @item e
% The closed loop poles of
% @iftex
% @tex
% $(A - B K)$.
% @end tex
% @end iftex
% @ifinfo
% (@var{a} - @var{b}@var{k}).
% @end ifinfo
% @end table
% @end deftypefn