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V.F.MONTAGNER , C.L.F.OLIVEIRA , T.R.CALLIERO , R.A.BORGES , P.L.D.PERES , C.PRIEUR

Robust absolute stability and stabilization based on homogeneous polynomially parameter-dependent Lur'e functions

Rapport LAAS No06617
2007 American Control Conference, New York (USA), 11-13 Juillet 2007, pp.6021-6026

Diffusable

This paper provides finite dimensional convex conditions to construct homogeneous polynomially parameterdependent Lur'e functions which ensure the stability of nonlinear systems with state-dependent nonlinearities lying in general sectors and which are affected by uncertain parameters belonging to the unit simplex. The proposed conditions are written as linear matrix inequalities parameterized in terms of the degree g of the parameter-dependent solution and in terms of the relaxation level d of the inequality constraints, based on an extension of Polya's Theorem. As g and d increase, progressive less conservative solutions are obtained. The results in the paper include as special cases existing conditions for robust stability analysis and for absolute stability. A convex solution for control design is also provided. Numerical examples illustrate the efficiency of the proposed conditions.

Affectations: Université de Campinas, Brésil ( Campinas ) Méthode et Algorithme en Commande ( MAC )


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