Exponential stability of singularly perturbed impulsive delay differential equations |
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| Authors: | Wei Zhu Daoyi Xu |
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| Affiliation: | a Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China
b Yangtze Center of Mathematics, Sichuan University, Chengdu, 610064, China |
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| Abstract: | In this paper, the exponential stability of singularly perturbed impulsive delay differential equations (SPIDDEs) is concerned. We first establish a delay differential inequality, which is useful to deal with the stability of SPIDDEs, and then by the obtained inequality, a sufficient condition is provided to ensure that any solution of SPIDDEs is exponentially stable for sufficiently small ε>0. A numerical example and the simulation result show the effectiveness of our theoretical result. |
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| Keywords: | Exponential stability Singularly perturbed delay differential equations (SPIDDEs) Delay differential inequality Sufficient condition |
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