CVX no feasable solution Yalmip got solution

1

Hello freinds, I am new to cvx, I am sure I am doing something wrong , any help is appreciated
Thank you

%%   CVX
clear all;
clc
%% Define Matrix
A1 = [0 1; 26.3679 -0.2839]; B1 = [0 -0.2633]'; C1 = [1 0];
A2 = [0 1; 25.7826 -0.2833]; B2 = [0 -0.2469]'; C2 = [1 0];
A3 = [0 1; 24.1023 -0.2818]; B3 = [0 -0.2002]'; C3 = [1 0];
A4 = [0 1; 21.5219 -0.2802]; B4 = [0 -0.1299]'; C4 = [1 0];

Ap = [0 0.0050; 0.1076 0.0014]; Bp = [0 0.0039]'; Cp = [0 0];

Q11 =[0.01 0; 0 0.01]; Q22 =[0.01 0; 0 0.01];

cvx_begin

    variable P22(2,2) symmetric;
    variable Z1(2,1);
    variable Z2(2,1);
    variable Z3(2,1);
    variable Z4(2,1);
    variable alpha(1,1);
%% Formulation of the LMI matrix 

U11 = [P22*A1+A1'*P22-Z1*C1-C1'*Z1'+Ap'*Ap+Q22            P22;
                        P22                  -alpha*eye(2)];

U22 = [P22*A2+A2'*P22-Z2*C2-C2'*Z2'+Ap'*Ap+Q22            P22;
                        P22                  -alpha*eye(2)];
                    
U33 = [P22*A3+A3'*P22-Z3*C3-C3'*Z3'+Ap'*Ap+Q22            P22;
                        P22                  -alpha*eye(2)];
                    
U44 = [P22*A4+A4'*P22-Z4*C4-C4'*Z4'+Ap'*Ap+Q22            P22;
                        P22                  -alpha*eye(2)];
                    
    minimize (alpha);
            subject to
            P22>=zeros(2);
            U11<=zeros(4);
            U22<=zeros(4);
            U33<=zeros(4);
            U44<=zeros(4);
cvx_end
2

As Yohan stated over on the YALMIP forum, you need to either invoke CVX with cvx_begin sdp in order to get your inequalities automatically interpreted as LMIs, or if not using that option, change them to

P22 == semidefinite(2);
-U11 == semidefinite(4);
-U22 == semidefinite(4);
-U33 == semidefinite(4);
-U44 == semidefinite(4);

Reading the CVX User’s Guide at http://cvxr.com/cvx/doc/CVX.pdf will help you in successfully using CVX.