stabilityTest.m

%% stability analysis under discrete time domain using cvx
sys1 = feedback(GcDis*GpDis,1);
sys2 = feedback(GcDis*GpDis*1.65,1);
[A1,B1,C1,D1] = ssdata(sys1);
[A2,B2,C2,D2] = ssdata(sys2);
n = size(A1,1);
cvx_begin sdp
variable P(n,n) symmetric
A1'*P*A1 - P <= eye(n)
A2'*P*A2 - P <= eye(n)
P >= eye(n)
cvx_end

%% stability analysis under continuous time domain using cvx

sys1 = ss(minreal(feedback(C*Gp,1)));
sys2 = ss(minreal(feedback(C*Gp*1.1,1)));
[A1,B1,C1,D1] = ssdata(sys1);
[A2,B2,C2,D2] = ssdata(sys2);

n = size(A1,1);
cvx_clear
cvx_begin sdp
cvx_precision high
variable P(n,n) symmetric
A1'*P + P*A1 < eye(n)
A2'*P + P*A2 < eye(n)
P > eye(n)
cvx_end
%% stability analysis under continuous time domain using LMI toolbox

sys1 = minreal(feedback(C*Gp,1));
sys2 = minreal(feedback(C*Gp*1.5,1));
[A1,B1,C1,D1] = ssdata(sys1);
[A2,B2,C2,D2] = ssdata(sys2);

n = size(A1,1);
setlmis([]) 
p = lmivar(1,[n 1]);
lmiterm([1 1 1 p],1,A1,'s');
lmiterm([-2 1 1 p],1,1);
lmiterm([3 1 1 p],1,A2,'s');
lmis = getlmis;
[tmin,xfeas] = feasp(lmis);
P = dec2mat(lmis,xfeas,p);

%% stability analysis under discrete time domain using LMI toolbox

sys1 = minreal(feedback(C*Gp,1));
sys2 = minreal(feedback(C*Gp*1.1,1));
[A1,B1,C1,D1] = ssdata(sys1);
[A2,B2,C2,D2] = ssdata(sys2);

n = size(A1,1);
setlmis([]) 
p = lmivar(1,[n 1]);
lmiterm([1 1 1 p],1,A1,'s');
lmiterm([1 1 2 0],1);
lmiterm([1 2 2 p],-1,1);
lmis = getlmis;
[tmin,xfeas] = feasp(lmis);
P = dec2mat(lmis,xfeas,p);