No feasible solution either using mosek,sdpt3-4 or ,sedumi for LMI problem

[David Rodriguez]

Hi I am implementing an example problem from a thesis so it definitely must have a solution but I cannot find the problem. I have tried all the debugging techniques recommended in the forum and yalmip page, check for errors in the inequalities (They are correctly written). The problem consists of designing a second order discrete H infinity robust controller for a polytopic system with 16 vertices using the following algorithm: I must add is my first time using Yalmip, sorry for any silly mistakes

based on this theorem and Lemma eq 3.53, 3.59

The example problem is the following :

I provide two codes and 1 data set. The fist code corresponds to the initialization of the algorithm which is to develop an initial second order Hinf controller using the command Hinfstruct. The second code corresponds to the iterative algorithm. The data set is the initialization data resulted from code1.

So the problem has no feasible solutions either for step 2 or step 3. Any mistakes  spotted in formulating the problem?

[Johan Löfberg]

already this is infeasible

F2=[X>0*eye(5)];

for i=1:2

F2 = [F2,PT{i}>=1e-3*eye(5)...

    [-A{i}'*PT{i}*A{i} + PT{i}, A{i}'*PT{i}+MT'-A{i}'*X, MT'*B{i}-A{i}'*X*B{i}, C{i}';...

    PT{i}*A{i}+MT-X*A{i}, -PT{i}+2*X, X*B{i}, zeros(size(PT{i},1),size(C{i},1));...

    B{i}'*MT-B{i}'*X*A{i}, B{i}'*X, eye(size(D{i},2)), D{i}';...

    C{i}, zeros(size(C{i},1),size(X,2)), D{i}, mu*eye(size(C{i},1))]>=0*eye(12)];

end

optimize(F2)

for i = 1:1 works