December 07, 2012, Webb 1100

Lyapunov’s second theorem is an essential tool for stability analysis of differential equations. We provide an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. The talk will be non technical and will concentrate on the motivations and potential of this approach for systems and control.Joint work with Fulvio Forni, based on http://arxiv.org/abs/1208.2943

Rodolphe Sepulchre is Professor and Chair of  the department of Electrical Engineering and Computer Science at the University of Liege, Belgium. He received his engineering degree and Ph.D. degree in applied mathematics from the University of Louvain, Belgium, in 1990 and 1994 respectively. He held various research and visiting positions at UCSB (1994-1996), Princeton (2002-2003), and Mines Paris-Tech (2009-2010).His main research interests include nonlinear control systems, optimization on matrix manifolds with applications to large-scale problems in linear algebra, and applications of dynamical systems, in particular in the area of rhythmic and collective behavior.He currently serves as an associate editor for the journals  SIAM J. of Control and Optimization, Mathematics of Control, Signals, and Systems, Journal of Nonlinear Science, and Systems and Control Letters. He is a fellow of the IEEE and the recipient of  the 2008 IEEE CSS Ruberti young researcher prize.