% -*- texinfo -*-
% @deftypefn {Function File} {[@var{k}, @var{g}, @var{gw}, @var{xinf}, @var{yinf}] =} hinfsyn (@var{asys}, @var{nu}, @var{ny}, @var{gmin}, @var{gmax}, @var{gtol}, @var{ptol}, @var{tol})
%
% @strong{Inputs} input system is passed as either
% @table @var
% @item asys
% system data structure (see @command{ss}, @command{sys2ss})
% @itemize @bullet
% @item controller is implemented for continuous time systems
% @item controller is @strong{not} implemented for discrete time systems (see
% bilinear transforms in @command{c2d}, @command{d2c})
% @end itemize
% @item nu
% number of controlled inputs
% @item ny
% number of measured outputs
% @item gmin
% initial lower bound on
% @iftex
% @tex
% $ { \cal H }_\infty $
% @end tex
% @end iftex
% @ifinfo
% H-infinity
% @end ifinfo
% optimal gain
% @item gmax
% initial upper bound on
% @iftex
% @tex
% $ { \cal H }_\infty $
% @end tex
% @end iftex
% @ifinfo
% H-infinity
% @end ifinfo
% Optimal gain.
% @item gtol
% Gain threshold. Routine quits when @var{gmax}/@var{gmin} < 1+tol.
% @item ptol
% poles with @code{abs(real(pole))}
% @iftex
% @tex
% $ < ptol \Vert H \Vert $
% @end tex
% @end iftex
% @ifinfo
% < ptol*|H|
% @end ifinfo
% (@var{H} is appropriate
% Hamiltonian) are considered to be on the imaginary axis.
% Default: 1e-9.
% @item tol
% threshold for 0. Default: 200*@code{eps}.
%
% @var{gmax}, @var{min}, @var{tol}, and @var{tol} must all be positive scalars.
% @end table
% @strong{Outputs}
% @table @var
% @item k
% System controller.
% @item g
% Designed gain value.
% @item gw
% Closed loop system.
% @item xinf
% @acronym{ARE} solution matrix for regulator subproblem.
% @item yinf
% @acronym{ARE} solution matrix for filter subproblem.
% @end table
%
% References:
% @enumerate
% @item Doyle, Glover, Khargonekar, Francis, @cite{State-Space Solutions
% to Standard}
% @iftex
% @tex
% $ { \cal H }_2 $ @cite{and} $ { \cal H }_\infty $
% @end tex
% @end iftex
% @ifinfo
% @cite{H-2 and H-infinity}
% @end ifinfo
% @cite{Control Problems}, @acronym{IEEE} @acronym{TAC} August 1989.
%
% @item Maciejowksi, J.M., @cite{Multivariable feedback design},
% Addison-Wesley, 1989, @acronym{ISBN} 0-201-18243-2.
%
% @item Keith Glover and John C. Doyle, @cite{State-space formulae for all
% stabilizing controllers that satisfy an}
% @iftex
% @tex
% $ { \cal H }_\infty $@cite{norm}
% @end tex
% @end iftex
% @ifinfo
% @cite{H-infinity-norm}
% @end ifinfo
% @cite{bound and relations to risk sensitivity},
% Systems & Control Letters 11, Oct. 1988, pp 167--172.
% @end enumerate
% @end deftypefn