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Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses

Author

Listed:
  • Ting Cai

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Pei Cheng

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

Abstract

This paper is concerned with stability analysis of discrete-time stochastic delay systems with impulses. By using the sums average value of the time-varying coefficients and the average impulsive interval, two sufficient criteria for exponential stability of discrete-time impulsive stochastic delay systems are derived, which are more convenient to be applied than those Razumikhin-type conditions in previous literature. Both p th moment asymptotic stability and p th moment exponential stability are considered. Finally, two numerical examples to illustrate the effectiveness.

Suggested Citation

  • Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:418-:d:502913
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    References listed on IDEAS

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    1. Peng, Shiguo & Jia, Baoguo, 2010. "Some criteria on pth moment stability of impulsive stochastic functional differential equations," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1085-1092, July.
    2. Cheng, Pei & Deng, Feiqi, 2010. "Global exponential stability of impulsive stochastic functional differential systems," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1854-1862, December.
    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. Zhang, Yu, 2017. "Global exponential stability of delay difference equations with delayed impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 183-194.
    5. 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.
    6. Chen, Guiling & van Gaans, Onno & Lunel, Sjoerd Verduyn, 2018. "Existence and exponential stability of a class of impulsive neutral stochastic partial differential equations with delays and Poisson jumps," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 7-18.
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    Cited by:

    1. Yunfeng Li & Pei Cheng & Zheng Wu, 2022. "Exponential Stability of Impulsive Neutral Stochastic Functional Differential Equations," Mathematics, MDPI, vol. 10(21), pages 1-17, November.

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