%---------------------------------------------------------------------------
%
%   Parameters of the UV-MRAC for the third order system of relative
%   degree one. This system includes an input disturbance and uncertain
%   nonlinear parameter (alpha,alpha^2).
%   Copied from the file uvmrac_parameters_final.m of the paper TAC'2001.
%
%   Parameters for the first example are now preceded by "%".
%
%   Rio de Janeiro, September 16, 2003.
%
%   Author: Jose' Paulo V. S. da Cunha
%
%---------------------------------------------------------------------------

% Reference model matrix:

Am= [-2 0; 0 -2];

% Uniform upper bound for the norm of the input disturbance:

bar_d = 5;

% Value for the uncertain parameter:

alpha = 0.35;

% Plant matrices:

Ap = diag([-1 1 1]);

%Bp = [1 -1; 1 0; 0 1]*diag([1 alpha]);

Bp = [1 -1; 1 0; 0 1]*inv([1,2;-2,1])*[1,2*(alpha^2);-2,alpha];

Cp = [-1 2 1; 1 -3 2];

Dp = zeros(2);

% Plant initial condition:

%xp0 = [-0.25; 0.25; 0.25];

xp0 = [-1; 1; 1]*(-10);

% Transpose of the nominal parameter matrix:

theta_nom = [ -0.99  -0.23 ;
               0.57  -0.11 ;
              -0.42  -0.34 ;
              -0.42  -0.34 ;
              -0.39  -1.03 ;
               1.41  -0.43 ;
               0.2    0.4  ;
              -0.4    0.2  ] ;

theta_nomT = theta_nom';

% Precompensation matrix:

Sp = eye(2);

% Modulation function coefficients:

%c1 = 6.9;

c1 = 17;

c2 = 0;

%c3 = 2.3;

c3 = 6.9;

%wdc = 2.3;

wdc = 2.8;

% Desired coefficient for finite-time convergence:

delta = 0.1;

% Resulting coefficient:

dd = c3 * wdc * bar_d + delta;