hi

i try to solve this lmi using CVX but it is infeasible. could you please check this m file.

x0 = [.5;.5]; %initial condition vector

A=[0 1;0 -10];

B=[0;1];

C=[4 0];

D=0;

E=[0.1;0.1];

Ts=.01;

%State-Space Model

sys = ss(A, B, C, D);

%discrete State-Space Model

sys_d = c2d(sys, Ts);

[Ad, Bd, Cd, Dd] = ssdata(sys_d);

%State-Space Model

%n = size(A,1);

Aaug=[Ad zeros(2,1);Cd eye(1,1)];

Baug=[Bd;zeros(1,1)];

Caug=[Cd zeros(1,1)];

Eaug=[E zeros(2,2);zeros(1,1) 0 -1];

n = size(Aaug,1);

%State-Space Model

cvx_begin sdp

variable sigmax

variable gamasq

variable S(n,n) symmetric

variable G(n,n)

variable F(1,n)

%minimize (gamasq)

%minimize (sigmax)

%subject to

S > 0

[G’+G-S zeros(n,n) zeros(n,n) G*Aaug’+F’ Baug’ G GCaug’;
zeros(n,n) eye(n,n) zeros(n,n) eye(n,n) zeros(n,n) zeros(n,1);
zeros(n,n) zeros(n,n) gamasq*eye(n,n) Eaug’ zeros(n,n) zeros(n,1);

Aaug

*G’+Baug*F eye(n,n) Eaug S zeros(n,n) zeros(n,1);

G’ zeros(n,n) zeros(n,n) zeros(n,n) sigmax

*eye(n,n) zeros(n,1);*

CaugG’ zeros(1,n) zeros(1,n) zeros(1,n) zeros(1,n) 1]>0

Caug

cvx_end

%sigma1=1/sigmax;

%sigma1=.254

P=inv(S);

K_LQR=(G*P);

%% LQR Simulation

open(‘moningeventcontcvx’);

while(~exist(‘moningeventcontcvx’))

pause(1);

end;