Analyse de stabilité et synchronisation des systèmes singulièrement perturbés

Abstract : This PhD thesis is dedicated to the study of stability and control design for singularly perturbed systems. In the first part, we introduce and analyze a general class of singularly perturbed linear hybrid systems, in which the slow or fast nature of the variables is mode-dependent. Our stability analysis is based on classical results of Lyapunov’s theory for singularly perturbed systems. A second part of this work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. To avoid the use of centralized information related to the interconnection network structure, the problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear systemaThis PhD thesis is dedicated to the study of stability and control design for singularly perturbed systems. In the first part, we introduce and analyze a general class of singularly perturbed linear hybrid systems, in which the slow or fast nature of the variables is mode-dependent. Our stability analysis is based on classical results of Lyapunov’s theory for singularly perturbed systems. A second part of this work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. To avoid the use of centralized information related to the interconnection network structure, the problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system
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Jihene Ben Rejeb. Analyse de stabilité et synchronisation des systèmes singulièrement perturbés. Automatique / Robotique. Université de Lorraine, 2017. Français. ⟨NNT : 2017LORR0117⟩. ⟨tel-01753836⟩

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