Dashkovskiy, Sergey (Univ. of Bremen), Rüffer, Björn Sebastian (Univ. Bremen), Wirth, Fabian R. (National Univ. of Ireland at Maynooth)

An ISS Lyapunov Function for Networks of ISS Systems

Scheduled for presentation during the Regular Session "Large Scale Systems" (MoA09), Monday, July 24, 2006, 10:50−11:15, Room J

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on April 23, 2024

Abstract

We consider a finite number of nonlinear systems interconnected in an arbitrary way. Under the assumption that each subsystem is input-to-state stable (ISS) regarding the states of the other subsystems as inputs we are looking for conditions that guarantee input-to-state stability of the overall system. To this end we aim to construct an ISS-Lyapunov function for the interconnection using the knowledge of ISS-Lyapunov functions of the subsystems in the network. Sufficient conditions of a small gain type are obtained under which an ISS Lyapunov function can be constructed. The ISS-Lyapunov function is then given explicitly, and guarantees that the network is ISS.