Strict Lyapunov functions for consensus under directed connected graphs
Elena Panteley, Direttore di Ricerca al Laboratoire des Signaux et Systèmes (L2S, Gif-sur-Yvette, FR), terrà un seminario dal titolo Strict Lyapunov functions for consensus under directed connected graphs.
Il seminario avrà luogo il prossimo 24/02/2022 in Aula Magna del DIAG e sarà fruibile in streaming via zoom a questo link .
Abstract. It is known that for consensus of systems interconnected under a general directed graph topology, a necessary and sufficient condition for consensus is that graph has at least one rooted spanning tree. We present an analog of the Lyapunov equation that characterizes the spanning-tree condition for directed graphs. We show how this Lyapunov-like equation that involves the graph’s Laplacian can be applied in the case of systems described by simple first and second-order integrators. As a result, we provide strict Lyapunov functions that ensure global exponential stability of the consensus manifold via direct constructive proof.
Biosketch. Elena Panteley received the M.Sc. and Ph.D. degrees in applied mathematics from the State University of St. Petersburg, St. Petersburg, Russia, in 1986 and 1997, respectively. From 1986 to 1998, she held a research position with the Institute for Problems of Mechanical Engineering, Russian Academy of Science, St. Petersburg. She is a Senior Researcher (Directeur de Recherche) at CNRS and a member of the Laboratoire des Signaux et Systèmes, where she is the head of the team MODESTY (Modelling, Estimation and Analysis of Systems). She is also co-chair of the International Graduate School of Control of the European Embedded Control Institute (EECI-IGSC). Her research interests include stability and control of nonlinear dynamical systems and network systems with applications to electromechanical and neuronal systems.