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Stabilization of stochastic functional differential systems with delayed impulses

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  • Fu, Xiaozheng
  • Zhu, Quanxin
  • Guo, Yingxin

Abstract

This paper is concerned with the stabilization problem for a class of stochastic functional differential system with delayed impulses. By applying a generalized comparison principle and the average dwell time method, some sufficient criteria for input-to-state stable (ISS) type and exponential stability properties are derived. The coefficients of the upper bound for the diffusion operator of Lyapunov functions are allowed to be time-varying, which improves the existing results greatly. Two numerical examples are presented to illustrate the effectiveness of the proposed results.

Suggested Citation

  • Fu, Xiaozheng & Zhu, Quanxin & Guo, Yingxin, 2019. "Stabilization of stochastic functional differential systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 776-789.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:776-789
    DOI: 10.1016/j.amc.2018.10.063
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    References listed on IDEAS

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    1. Xu, Yong & Pei, Bin & Guo, Guobin, 2015. "Existence and stability of solutions to non-Lipschitz stochastic differential equations driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 398-409.
    2. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    3. Fengqi Yao & Feiqi Deng & Pei Cheng, 2013. "Exponential Stability of Impulsive Stochastic Functional Differential Systems with Delayed Impulses," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, April.
    4. Kao, Yonggui & Zhu, Quanxin & Qi, Wenhai, 2015. "Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 795-804.
    5. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
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    Cited by:

    1. Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Zhu, Ruiyuan & Guo, Yingxin & Wang, Fei, 2020. "Quasi-synchronization of heterogeneous neural networks with distributed and proportional delays via impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Cao, Wenping & Zhu, Quanxin, 2021. "Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    4. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.

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