Asymptotic properties of Zeno solutions

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.