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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. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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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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