% -*- texinfo -*-
% @deftypefn {Function File} {} dhinfdemo
% Demonstrate the functions available to design a discrete
% @iftex
% @tex
% $ { \cal H }_\infty $
% @end tex
% @end iftex
% @ifinfo
% H-infinity
% @end ifinfo
% controller. This is not a true discrete design. The
% design is carried out in continuous time while the effect of sampling
% is described by a bilinear transformation of the sampled system.
% This method works quite well if the sampling period is 'small'
% compared to the plant time constants.
%
% Continuous plant:
% @iftex
% @tex
% $$ G(s) = { 1 \over (s+2) (s+1) } $$
% @end tex
% @end iftex
% @ifinfo
% @example
% @group
% 1
% G(s) = --------------
% (s + 2)(s + 1)
% @end group
% @end example
% @end ifinfo
%
% Discretised plant with @acronym{ZOH} (Sampling period = @var{Ts} = 1 second):
% @iftex
% @tex
% $$ G(z) = { 0.39958z + 0.14700 \over (z - 0.36788) (z - 0.13533) } $$
% @end tex
% @end iftex
% @ifinfo
% @example
% @group
% 0.39958z + 0.14700
% G(z) = --------------------------
% (z - 0.36788)(z - 0.13533)
% @end group
% @end example
% @end ifinfo
%
% @example
% @group
% +----+
% -------------------->| W1 |---> v1
% z | +----+
% ----|-------------+ | T | => min.
% | | vz infty
% | +---+ v +----+
% *--->| G |--->O--*-->| W2 |---> v2
% | +---+ | +----+
% | |
% | +---+ |
% -----| K |<-------
% +---+
% @end group
% @end example
%
% @noindent
% W1 and W2 are the robustness and performancs weighting functions.
% @end deftypefn