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Analyse en stabilité et synthèse de lois de commande pour des systèmes polynomiaux saturants

Giorgio Valmorbida 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : We study the class of nonlinear dynamical systems which vector field is defined by polynomial functions. A large set of systems can be modeled using such class of functions. Tests for stability are formulated as semidefinite programming problems by considering positive polinomials to belong to the class of Sum of Squares polynomials. Polynomial control law gains are computed based on a linear change of coordinates and guarantee the local stability of the closed-loop system. Lyapunov theory is then applied in order to obtain estimates of the region of attraction for stable equilibrium points. Such estimates are given by level sets of polynomial positive functions.
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Submitted on : Monday, August 30, 2010 - 9:25:26 AM
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Giorgio Valmorbida. Analyse en stabilité et synthèse de lois de commande pour des systèmes polynomiaux saturants. Mathématiques [math]. INSA de Toulouse, 2010. Français. ⟨tel-00512335⟩

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