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Sur la stabilité robuste de systèmes linéaires: une approche par des fonctions dépendantes de paramètres

Valter Jùnior de Souza Leite 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This work deals with the application of parameter dependent Lyapunov and Lyapunov-Krasovskii functionals to some selected problems of robust control : robust D-stability of polytopes of matrices, robust D-stability of polytopes of polynomial matrices, robust stability of uncertain neutral systems with time-varying delays and robust H control of uncertain discrete time delay systems. The polytopic representation is used to describe the uncertainties. Convex formulations are obtained, in terms of linear matrix inequalities, that are sufficient for the solution of the selected problems. Those conditions can be solved in a efficient way through specialized interior point algorithms. The obtained results are less conservative than those from the literature, in general based on quadratic stability, i.e., the matrices in the functionals are fixed and do not depend on the uncertainty.
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Valter Jùnior de Souza Leite. Sur la stabilité robuste de systèmes linéaires: une approche par des fonctions dépendantes de paramètres. Mathématiques [math]. INSA de Toulouse, 2005. Français. ⟨tel-00149408⟩

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