Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems

Directeur de thèse :     Christophe PRIEUR

École doctorale : Electronique, electrotechnique, automatique, traitement du signal (EEATS)

Spécialité : Automatique et productique

Structure de rattachement : Grenoble-INP

Établissement d'origine : INPG

Financement(s) : Contrat doctoral

Date d'entrée en thèse : 01/10/2012

Date de soutenance : 18/09/2015

Composition du jury :
Sophie TARBOURIECH - Rapporteur - Directeur de recherche, LAAS-CNRS
Joseph WINKIN - Rapporteur - Professeur, Université de Namur
Florent DI MEGLIO - Examinateur - Enseignant chercheur, Centre Automatique et Systèmes MINES ParisTech
Didier GEORGES - Examinateur - Professeur, Grenoble INP
Paola GOATIN - Examinateur - Directeur de recherche, INRIA Sophia-Antipolis-Méditerranée
Christophe PRIEUR - Directeur de thèse - Directeur de recherche, Gipsa-lab CNRS
Antoine GIRARD - CoDirecteur de thèse - Maître de Conférences, Université Joseph Fourier

Résumé : The present thesis is concerned with a class of linear hyperbolic systems with multiple time scales modeled by a small perturbation parameter. Firstly, we study a class of singularly perturbed linear hyperbolic systems. By setting the perturbation parameter to zero, the two subsystems, namely the reduced subsystem and the boundary-layer subsystem, are formally computed. The link in terms of the stability between the full system and the subsystems is established. Moreover, under certain conditions, the Tikhonov approximation for such systems is achieved by Lyapunov method. Secondly, we consider coupled ODE-PDE systems with two time scales. The stability between the full system and both subsystems is studied. The Tikhonov theorem for such coupled ODE-PDE systems is proved by means of a Lyapunov function. Finally, the boundary control synthesis based on singular perturbation method is used to design a new control strategy for different applications.