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) GAaug’+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) gamasqeye(n,n) Eaug’ zeros(n,n) zeros(n,1);
AaugG’+BaugF eye(n,n) Eaug S zeros(n,n) zeros(n,1);
G’ zeros(n,n) zeros(n,n) zeros(n,n) sigmaxeye(n,n) zeros(n,1);
CaugG’ zeros(1,n) zeros(1,n) zeros(1,n) zeros(1,n) 1]>0
cvx_end
%sigma1=1/sigmax;
%sigma1=.254
P=inv(S);
K_LQR=(G*P);
%% LQR Simulation
open(‘moningeventcontcvx’);
while(~exist(‘moningeventcontcvx’))
pause(1);
end;