Einladung zum Vortrag im Kolloquium Technische Kybernetik

Small Gain Theorems and Construction of ISS Lyapunov Functions for Interconnected Systems

Prof. Fabian Wirth
Institut für Mathematik
Universität Würzburg

    Zeit: Dienstag 28.04.2009 · 16:00 Uhr
    Ort: Seminarraum IST 3.243 · Pfaffenwaldring 9 · Campus Stuttgart-Vaihingen

Abstract

We consider a network consisting of n interconnected nonlinear subsystems. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. In this setup a gain matrix may be used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, we construct a locally Lipschitz continuous ISS Lyapunov function for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems.

Biographical Information

Fabian Wirth received his PhD in mathematics with the Institute for Dynamical Systems at the University of Bremen in 1995. He has since been working in the areas of stability theory and robust stability of linear time-varying, nonlinear and hybrid systems. Since September 2007 he is Professor for Mathematics at the University of Würzburg. Previously he has held positions in Bremen, Frankfurt and at the Hamilton Institute in Maynooth, Ireland. In the latter position he has started working in the area of congestion control and on the modelling of TCP. His current interests include mathematical modelling of the dynamics given by a communication protocol, modelling of logistic networks and control over communication channels. Fabian Wirth is associate editor of Systems and Control Letters and the SIAM Journal on Control and Optimization.