%% Finite-dimensional Koopman linearization
% Example from the Data-driven Science and Engineering book by Brunton &
% Kutz, 2019, page 262.

%% Parameters
lambda = 1;
mu = -0.1;

x0 = [-6; 6];    

%% Linearization of the nonlinear model at [0; 0] 

A1 = [mu 0; 0 lambda];
B1 = [0; 1];
C1 = eye(2,2);
D1 = zeros(2,1);

%% Koopman (global) linearization 

A2 = [mu 0 0; 0 lambda -lambda; 0 0 2*mu];
B2 = [0; 1; 0];
C2 = [1 0 0; 0 1 0];
D2 = zeros(2,1);

%% LQR design for the linearized model

Q1 = 10*eye(2,2);
R1 = 1;

K1 = lqr(A1,B1,Q1,R1)

%% LQR design for the Koopman model

Q2 = 10*eye(3,3); Q2(3,3) = 0;
R2 = 1;

K2 = lqr(A2,B2,Q2,R2)