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Didier Henrion(henrionlaas.fr) Abstract: Following a polynomial approach, many robust fixedorder controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner approximations modelled by a single polynomial sublevel set. Those inner approximations converge in a strong analytic sense to the nonconvex original feasible set, with asymptotically vanishing conservatism. One may also impose the hierarchy of inner approximations to be nested or convex. In the latter case they do not converge any more to the feasible set, but they can be used in a convex optimization framework at the price of some conservatism. Finally, we show that the specific geometry of nonconvex polynomial stability regions can be exploited to improve convergence of the hierarchy of inner approximations. Keywords: Polynomial matrix inequality, linear matrix inequality, robust optimization, linear controller design, moments, positive polynomials Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Robust Optimization Citation: Download: [PDF] Entry Submitted: 04/26/2011 Modify/Update this entry  
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