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arXiv · 1610.01403

Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems

Andrii Mironchenko·Guosong Yang·Daniel Liberzon
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Abstract

We prove a novel Lyapunov-based small-gain theorem for networks of $ n \geq 2 $ 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. We also show how 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 the derived small-gain theorems.

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Andrii Mironchenko, Guosong Yang, Daniel Liberzon. 2016-10-05. Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems. https://arxiv.org/abs/1610.01403

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