Séminaire d'Automatique du Plateau de Saclay : Necessary and sufficient condition for exponential synchronization of nonlinear systems

Séminaire le 30 Novembre 2017, 11h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Vincent Andrieu (CNRS Researcher, LAGEP-CNRS, Université de Lyon 1, France)

Based on recent works on transverse exponential stability, some necessary and sufficient conditions for the existence of a (locally) exponential synchronizer are established. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turns, is also equivalent to the existence of a symmetric covariant tensor field which satisfies a kind of Lyapunov inequality. Based on this property, we provide the construction of such synchronizer. We discuss then the possibility to achieve global synchronization.

Bio. Vincent Andrieu graduated in applied mathematics from “INSA de Rouen”, France, in 2001. After working in ONERA (French aerospace research company), he obtained a PhD degree from “Ecole des Mines de Paris” in 2005. In 2006, he had a research appointment at the Control and Power Group, Dept. EEE, Imperial College London. In 2008, he joined the CNRS-LAAS lab in Toulouse, France, as a “CNRS-chargé de recherche”. Since 2010, he has been working in LAGEP-CNRS, Université de Lyon 1, France. In 2014, he joined the functional analysis group from Bergische Universitäte Wuppertal in Germany, for two sabbatical years. His main research interests are in the feedback stabilization of controlled dynamical nonlinear systems and state estimation problems. He is also interested in practical application of these theoretical problems, and especially in the field of aeronautics and chemical engineering.