LQR through LMI (using msfsyn)

Hello,

I am trying to synthetize an LQR controller solving the problem as linear programming with LMI constraints (using MATLAB function msfsyn). The algorithm works fine only with small values of matrix Q. As soon as I increase the state weight (in matrix Q) MATLAB returns the LMI optimization problem is unfeasible. Any suggestion? Is it a numerical problem? Any way to solve it?

Attached the script I am using. For Q(1) = 10 it works fine. For Q(1) = 1e10 the problem is unfeasible.

Thanks.

Andrea