Lyapunov small-gain theorems for not necessarily ISS hybrid systems

Titelangaben

Mironchenko, Andrii ; Yang, Guosong ; Liberzon, Daniel:
Lyapunov small-gain theorems for not necessarily ISS hybrid systems.
In: Proceedings of 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). - Groningen, The Netherlands : University of Groningen Press , 2014 . - S. 1001-1008
ISBN 978-90-367-6321-9

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Abstract

We prove a novel Lyapunov-based small-gain theorem for interconnections of n hybrid systems, which are not necessarily input-to-state stable. This result unifies and extends several small-gain theorems for hybrid and impulsive systems, proposed in the last few years. Also we show how the average dwell-time (ADT) clocks and reverse ADT clocks can be used to modify the Lyapunov functions for subsystems and to enlarge the applicability of derived small-gain theorems.