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Convergent relaxations of polynomial matrix inequalities and static output feedback

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2 Author(s)
Henrion, D. ; LAAS-CNRS, Toulouse, France ; Lasserre, J.-B.

Using a moment interpretation of recent results on sum-of-squares decompositions of nonnegative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve nonconvex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to the global optimum. Results from the theory of moments are used to detect whether the global optimum is reached at a given LMI relaxation, and if so, to extract global minimizers that satisfy the PMI. The approach is successfully applied to PMIs arising from static output feedback design problems.

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Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 2 )