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Convergent relaxations of polynomial matrix inequalities and static output feedback

Didier Henrion (henrion***at***laas.fr)
Jean B. Lasserre (lasserre***at***laas.fr)

Abstract: Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex 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.

Keywords: Polynomial matrix, nonconvex optimization, convex optimization, static output feedback design

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Applications -- Science and Engineering (Control Applications )

Citation: LAAS-CNRS Research Report, November 2004, submitted for publication.

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Entry Submitted: 11/15/2004
Entry Accepted: 11/15/2004
Entry Last Modified: 11/15/2004

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