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Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach
Author(s) -
Li Dianqiang,
Cheng Pei,
He Shuping
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4297
Subject(s) - infimum and supremum , mathematics , interval (graph theory) , exponential stability , exponential function , lyapunov function , control theory (sociology) , stability (learning theory) , nonlinear system , sequence (biology) , stochastic differential equation , mathematical analysis , computer science , physics , control (management) , combinatorics , quantum mechanics , artificial intelligence , machine learning , biology , genetics
In this paper, we aim to investigate the exponential stability of general hybrid stochastic functional differential systems with delayed impulses. By using the average impulsive interval and the Lyapunov function method, we derive some sufficient conditions for exponential stability, which are less conservative than those existing results based on the supremum or infimum of impulsive interval and more convenient to be applied than those Razumikhin‐type conditions in the literature. Meanwhile, we show that unstable hybrid stochastic delay differential systems, both linear and nonlinear, can be stabilized by suitably impulsive sequence. Finally, two examples are discussed to illustrate the effectiveness and advantages of the obtained results. Copyright © 2017 John Wiley & Sons, Ltd.