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Une contribution à la modélisation et à la commande des systèmes non linéaires à commutation

Abstract : The focus of this work is the stability analysis of nonlinear
switched systems, which can be considered as a high level abstraction of hybrid systems. Five different chapters are devoted to this issue. After a general introduction, the second chapter proposes an algorithm to control the commutations, which ensures the conditional stability. The approach lies on the representation of the non linearities by a polytopic description. Then, some sufficient conditions are given by several matrix inequalities. The next chapter presents a necessary and sufficient condition to guarantee the uniform stabilization of the switched system. This condition is based on a new notion: the common control Lyapunov function, which is used to have an explicit stabilizing control law. In the fourth chapter, we introduce a new formal model to represent switched systems in which some switchings are forbidden by the physics of the systems. The structure is composed of a switched system and a Time Petri Nets whose analysis is used to characterize all the allowed switching laws. Then, different stability tools are applied to this kind of hybrid systems. In the last chapter, we propose a new approach of the control of switched
systems. The problem is tackled without a complete description of the sub-dynamics and even without knowing the switching signal. The proposed control design methodology is based on fast estimations of derivatives and parameters. The proposed algorithm
ensures the practical stability, if the time between commutations is not too small, even if the signals are disturbed.
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https://tel.archives-ouvertes.fr/tel-00259420
Contributor : Romain Bourdais Connect in order to contact the contributor
Submitted on : Thursday, February 28, 2008 - 9:40:33 AM
Last modification on : Saturday, December 18, 2021 - 3:01:54 AM
Long-term archiving on: : Thursday, May 20, 2010 - 8:04:24 PM

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  • HAL Id : tel-00259420, version 1

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Romain Bourdais. Une contribution à la modélisation et à la commande des systèmes non linéaires à commutation. Automatique / Robotique. Ecole Centrale de Lille, 2007. Français. ⟨tel-00259420⟩

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