Journal
NONLINEAR ANALYSIS-HYBRID SYSTEMS
Volume 30, Issue -, Pages 256-265Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.nahs.2018.06.005
Keywords
Hybrid dynamical system; Zeno behavior; Asymptotic stability
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This paper is concerned with problems related to Zeno solutions in hybrid dynamical systems. Zeno phenomenon is characterized by infinitely many impulses over a finite period of time and leads to a bounded time domain of solutions. Since an unbounded time domain for solutions is crucial for many applications, a method to prolong solutions to the hybrid dynamical system beyond its Zeno time is proposed in this paper. Moreover, we propose a way for asymptotic characterization of the prolonged solutions. We introduce a new concept of asymptotic stability with respect to a closed set for hybrid systems with Zeno solutions and provide sufficient conditions to verify it. The examples illustrate the proposed approach. (C) 2018 Elsevier Ltd. All rights reserved.
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