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Stabilization of linear impulsive systems through a nearly-periodic reset

Laurentiu Hetel 1 Jamal Daafouz 2, 3 Sophie Tarbouriech 4 Christophe Prieur 5 
1 SyNeR - Systèmes Non Linéaires et à Retards
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
4 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This paper deals with the class of impulsive systems constituted by a continuous-time linear dynamics for all time, except at a sequence of instants. When such a discrete time occurs, the state undergoes a jump, or more precisely follows a discrete linear dynamics. The sequence of time instants, when a discrete dynamics occurs, is nearly-periodic only, i.e. it is distant from a periodic sequence to an uncertain error. This paper succeeds to state tractable conditions to analyze the stability, and to design reset matrices such that the hybrid system is globally exponentially stable to the origin. The approach is based on a polytopic embedding of the uncertain dynamics. Some examples illustrate the main results.
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Submitted on : Monday, September 24, 2012 - 1:51:08 PM
Last modification on : Wednesday, September 7, 2022 - 8:14:05 AM

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Laurentiu Hetel, Jamal Daafouz, Sophie Tarbouriech, Christophe Prieur. Stabilization of linear impulsive systems through a nearly-periodic reset. Nonlinear Analysis: Hybrid Systems, Elsevier, 2013, 7 (1), pp.4-15. ⟨10.1016/j.nahs.2012.06.001⟩. ⟨hal-00734728⟩

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