Constructions of ISS-Lyapunov functions for interconnected impulsive systems

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Dashkovskiy, Sergey ; Mironchenko, Andrii:
Constructions of ISS-Lyapunov functions for interconnected impulsive systems.
In: 51st IEEE Conference on Decision and Control (CDC) : Proceedings. - Piscataway, NJ, USA : IEEE , 2012 . - S. 6831-6836
ISBN 978-1-4673-2065-8
DOI: https://doi.org/10.1109/CDC.2012.6426871

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Abstract

In this paper we provide two small-gain theorems for impulsive systems. The first of them provides a construction of an ISS-Lyapunov function for interconnections of impulsive systems if ISS-Lyapunov functions for subsystems are given and a small-gain condition holds. If, in addition, these given ISS-Lyapunov functions are exponential then the second theorem provides a construction of an exponential ISS-Lyapunov function for the interconnection if the gains are power functions.