%% Example 6.11 from J.B.Burl: Linear optimal control.
% Equations of a satellite tracking antenna

A = [0 1; 0 -0.1];
Bu = [0; 0.001];
Bw = [0; 0.001];

Sw = 50000;

Q = [180 0; 0 0];
R = 1;

[S,D,K] = care(A,Bu,Q,R);

Cx = lyap(A-Bu*K,Bw*Sw*Bw')
sigma_theta = sqrt(Cx)

%% Simulation in Simulink

tc = 0.001; % correlation time
piw = tc*Sw; % noise power