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Sur la stabilité locale de systèmes linéaires avec saturation des commandes

Abstract : The aim of this thesis is the study of the local asymptotic stability of discrete-time linear systems subject to control saturation. The work is developed by using two representations of the closed-loop saturated system, namely by regions of saturation and by polytopic model. The analysis of the stability of the closed-loop saturated system as well as the synthesis of saturating control laws are based on the concept of contractive sets. In this context, new results are proposed by considering two distinct approaches. The first one deals with polyhedral sets. The contractivity of the trajectories of the saturated system in polyhedral sets is studied. By considering the representation by regions of saturation, necessary and sufficient conditions are stated for the polyhedral contractivity with respect to the trajectories of the saturated system. From the representation by polytopic model only sufficient conditions are stated. The conditions obtained with both approaches lead to the formulation of algorithms to determine polyhedral domains of asymptotic stability and non-linear behavior for the closed-loop system. These algorithms are based on linear programming. The second approach deals with ellipsoidal sets and considers the polytopic representation of the saturated system. A sufficient condition for the contractivity of ellipsoids with respect to the trajectories of the closed-loop system are formulated in terms of linear matrix inequalities (LMIs). From this condition, an algorithm to compute approximations of the basin of attraction of the origin of the closed-loop system is proposed. This algorithm is based on the solution of convex optimization problems. On the other hand, given a set of initial admissible conditions X0, an LMI-based framework is proposed to compute saturating control laws that ensure the asymptotic convergence to the origin of all the trajectories emanating from X0.
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Submitted on : Friday, September 9, 2005 - 10:41:34 AM
Last modification on : Friday, January 10, 2020 - 9:08:09 PM
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  • HAL Id : tel-00010086, version 1


Joâo Manoel Gomes da Silva. Sur la stabilité locale de systèmes linéaires avec saturation des commandes. Automatique / Robotique. Université Paul Sabatier - Toulouse III, 1997. Français. ⟨tel-00010086⟩



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