Einladung zum Vortrag im Kolloquium
Small Gain Theorems and Construction of ISS
Lyapunov Functions for Interconnected Systems
Prof. Fabian Wirth
Institut für Mathematik
Zeit: Dienstag 28.04.2009
· 16:00 Uhr
Ort: Seminarraum IST 3.243 · Pfaffenwaldring 9 · Campus
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.
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
modelling of the dynamics given by a communication protocol, modelling
networks and control over communication channels.
Fabian Wirth is associate editor of Systems and Control Letters and the
SIAM Journal on
Control and Optimization.