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solve an inequality with LMI approach

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haifa
haifa 2014-2-1
评论： Johan Löfberg 2014-2-5
I would like to solve this inequality :
Q*A'+A*Q+L'*B'+B*L < 0
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Matt J
Matt J 2014-2-5
Does L<0 mean that L(i,j)<0 for all i,j ?

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Johan Löfberg
Johan Löfberg 2014-2-5
编辑：Johan Löfberg 2014-2-5
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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