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Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency

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  • Zhao, Yongshun
  • Li, Xiaodi
  • Cao, Jinde

Abstract

This paper investigates the global exponential stability of impulsive systems with infinite distributed delay. By introducing two auxiliary functions and two essential lemmas, some sufficient conditions of stability are presented based on flexible impulse frequency, where impulses are considered as perturbations. When the interval between two consecutive impulse times is very small in some time domains, our result just asks that it meets our proposed conditions, which is different from some exist results. The effectiveness of our result is demonstrated through Two simulation examples.

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  • Zhao, Yongshun & Li, Xiaodi & Cao, Jinde, 2020. "Global exponential stability for impulsive systems with infinite distributed delay based on flexible impulse frequency," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304227
    DOI: 10.1016/j.amc.2020.125467
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    References listed on IDEAS

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    1. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
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    7. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
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    Cited by:

    1. Yujuan Tian & Yuhan Yin & Fei Wang & Kening Wang, 2022. "Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
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    4. Liu, Haoliang & Zhang, Taixiang & Li, Xiaodi, 2021. "Event-triggered control for nonlinear systems with impulse effects," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

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