Existence of solution, pulse phenomena and stability criteria for state-dependent impulsive differential equations with saturation

摘要

This paper discusses the problem of the state-dependent impulsive differential equations (SDIDE) with saturation. First, the existence of solution for the system and some sufficient conditions which can be guaranteed every solution intersecting each impulsive surface exactly once are derived. Second, combining with comparison principle and some inequality techniques, we give some local quasi-exponential stability for SDIDE with saturation. Moreover, this paper proposes some succinct results by comparing to those for fixed time impulsive dynamical systems. Finally, some examples with simulations are given to demonstrate the effectiveness of our results. (C) 2019 Elsevier B.V. All rights reserved.