IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v421y2022ics0096300322000364.html
   My bibliography  Save this article

Stability of stochastic nonlinear delay systems with delayed impulses

Author

Listed:
  • Cao, Wenping
  • Zhu, Quanxin

Abstract

In this paper, we study the input-to-state stability of a class of stochastic delay differential equations with delay impulses. We consider the two cases where the continuous stochastic delay system is stable and unstable, and establish different types of stability conditions by using the average dwell time and the vector Lyapunov function method. Finally, two examples are used to verify the validity of our results.

Suggested Citation

  • Cao, Wenping & Zhu, Quanxin, 2022. "Stability of stochastic nonlinear delay systems with delayed impulses," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000364
    DOI: 10.1016/j.amc.2022.126950
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322000364
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.126950?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Hu, Rong, 2020. "Almost sure exponential stability of the Milstein-type schemes for stochastic delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. 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.
    4. Fu, Xiaozheng & Zhu, Quanxin, 2020. "Exponential stability of neutral stochastic delay differential equation with delay-dependent impulses," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    5. Wang, Xiaohu & Guo, Qingyi & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1698-1710.
    6. Wan, Fangzhe & Hu, Po & Chen, Huabin, 2020. "Stability analysis of neutral stochastic differential delay equations driven by Lévy noises," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    7. Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mingli Xia & Linna Liu & Jianyin Fang & Yicheng Zhang, 2023. "Stability Analysis for a Class of Stochastic Differential Equations with Impulses," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    2. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Liu, Yiqun & Zhuang, Guangming & Zhao, Junsheng & Lu, Junwei & Wang, Zekun, 2023. "H∞.. admissibilization for time-varying delayed nonlinear singular impulsive jump systems based on memory state-feedback control," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    4. Faisal Altaf & Ching-Lung Chang & Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Chi-Min Shu & Ahmad H. Milyani, 2022. "Adaptive Evolutionary Computation for Nonlinear Hammerstein Control Autoregressive Systems with Key Term Separation Principle," Mathematics, MDPI, vol. 10(6), pages 1-20, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    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. 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.
    4. Liu, Jiamin & Li, Zhao-Yan & Deng, Feiqi, 2021. "Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    5. Li, Liangliang & Jian, Jigui, 2015. "Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 860-873.
    6. Li, Dingshi & He, Danhua & Xu, Daoyi, 2012. "Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1531-1543.
    7. Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    8. Long, Shujun & Wang, Xiaohu & Li, Dingshi, 2012. "Attracting and invariant sets of non-autonomous reaction-diffusion neural networks with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2199-2214.
    9. Peng, Dongxue & Li, Xiaodi & Rakkiyappan, R. & Ding, Yanhui, 2021. "Stabilization of stochastic delayed systems: Event-triggered impulsive control," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    10. Wang, Xin & Zhuang, Guangming & Chen, Guoliang & Ma, Qian & Lu, Junwei, 2022. "Asynchronous mixed H∞ and passive control for fuzzy singular delayed Markovian jump system via hidden Markovian model mechanism," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    11. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    12. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    13. Gao, Shuaibin & Li, Xiaotong & Liu, Zhuoqi, 2023. "Stationary distribution of the Milstein scheme for stochastic differential delay equations with first-order convergence," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    14. 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.
    15. Sabermahani, Sedigheh & Ordokhani, Yadollah, 2021. "General Lagrange-hybrid functions and numerical solution of differential equations containing piecewise constant delays with bibliometric analysis," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    16. Caraballo, Tomás & Belfeki, Mohsen & Mchiri, Lassaad & Rhaima, Mohamed, 2021. "h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    17. Zhang, Yutian & Luo, Qi, 2012. "Novel stability criteria for impulsive delayed reaction–diffusion Cohen–Grossberg neural networks via Hardy–Poincarè inequality," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1033-1040.
    18. 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.
    19. Lijun Pan & Jinde Cao & Yong Ren, 2020. "Impulsive Stability of Stochastic Functional Differential Systems Driven by G-Brownian Motion," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    20. Yu, Peilin & Deng, Feiqi & Sun, Yuanyuan & Wan, Fangzhe, 2022. "Stability analysis of impulsive stochastic delayed Cohen-Grossberg neural networks driven by Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 434(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000364. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.