% Define the transfer functions
kd = 1.5;
tau = 1e2;
G = tf(kd, [tau 1]);

s = tf('s');
Gd = exp(-30*s);

% Approximate the transportaion delay Gd by Pade approximation
% Gd = pade(...)

% Define shaping cost filters
% ...

% Define the system matrix P - model with
%   Inputs:     exogenous signals (d),
%               control signals (u1 and u2)
%   Outputs:    appropriate error signals
%               measured outputs (y1 and y2)
P = [];

% Find the minimal realization of P (just to reduce the order of the resulting controller)
% P = minreal(P);

% Call hinfsyn to find the optimal controller
% K = hinfsyn(...);
K = zeros(2);

%% Plot the responses to the unit step on the disturbance input
% Define the transfer function from inputs [d, u1, u2] to outputs [y1, y2,
% u1, u2, y1, y2]. Only the last two inputs and outputs are used by the
% controller hence after closing the loop the model has only one input (d)
% and four inputs (y1, y2, u1 and u2).
P_du2yu = [Gd*G Gd*G 0; Gd*G*G Gd*G*G Gd*G; 0 1 0;0 0 1; Gd*G Gd*G 0; Gd*G*G Gd*G*G Gd*G];
set(P_du2yu, 'InputName', {'d', 'u1', 'u2'},...
    'OutputName', {'y1', 'y2', 'u1', 'u2', '_y1', '_y2'});
CL = lft(P_du2yu, K);
figure(1)
step(CL, 1000);