solve an inequality with LMI approach
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I would like to solve this inequality :
Q*A'+A*Q+L'*B'+B*L < 0
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Johan Löfberg
il 5 Feb 2014
Modificato: Johan Löfberg
il 5 Feb 2014
With the MATLAB Toolbox YALMIP, and some SDP solver installed (such as SDPT3, SeDuMi, Mosek etc) it would be (you have not clearly said which variables are decision variables, I assume Q (psd) and L (arbitrary))
Q = sdpvar(n,n);
L = sdpvar(m,n,'full');
Constraints = [Q >=0, Q*A'+A*Q+L'*B'+B*L <= 0];
solvesdp(Constraints);
The model is ill-posed though as Q and L arbitrarily close to zero is feasible, which means trouble in practice. Dehomogenioze it, for instance
Constraints = [Q >=0, Q*A'+A*Q+L'*B'+B*L <= -eye(n)];
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