LMI_Algebraic_Ricatti_Equations

clc; clear; close all;

%variables
P = sdpvar(2);
Q = sdpvar(2);
R = sdpvar(2,2);

%Data available
A = [1 2;
     2 4];
B = [1 0;0 2];
N = [3 2; 0 0];
 
%LMIs
LMI1 = [A'*P+P*A+Q P*B+N';
       (P*B+N')'  R ] >= 0;
LMIs = [ P > 0, Q >= 0, R >0, LMI1];
optimize (LMIs)

%Result
value(P)