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Sur la stabilité des systèmes à réinitialisation

Thomas Loquen 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Hybrid controllers are flexible tools for achieving system stabilization and/or performance improvement tasks. More particularly, hybrid controllers enrich the spectrum of achievable trade-offs. Indeed, the interaction of continuous- and discrete-time dynamics in a hybrid controller leads to rich dynamical behavior and phenomena not encountered in purely continuous-time system. Reset control systems are a class of hybrid controllers whose states are reset depending on an algebraic condition. In this thesis, we propose constructive conditions (Linear Matrix Inequalities) to analyze stability and performance level of a closed-loop system including a reset element. More particularly, we consider a magnitude saturation which could be the source of undesirable effects on these performances, including instability. Proposed results estimate the stability domain and a performance level of such a system, by using Lyapunov-like approaches. Constructive algorithms are obtained by exploiting properties of quadratic - or piecewise quadratic - Lyapunov functions. Beyond analysis results, we propose design methods to obtain a stability domain as large as possible. Design methods are based on both continuous-time approaches (anti-windup compensator) and hybrid-time approaches (design of adapted reset rules).
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Contributor : Arlette Evrard <>
Submitted on : Wednesday, February 16, 2011 - 1:31:26 PM
Last modification on : Thursday, June 10, 2021 - 3:06:50 AM
Long-term archiving on: : Tuesday, May 17, 2011 - 2:53:03 AM


  • HAL Id : tel-00566461, version 1


Thomas Loquen. Sur la stabilité des systèmes à réinitialisation. Mathematics [math]. Institut National Polytechnique de Toulouse - INPT, 2010. English. ⟨tel-00566461⟩



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