IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2012y2012i1n678536.html

Exponential Stability of Impulsive Stochastic Functional Differential Systems

Author

Listed:
  • Zheng Wu
  • Hao Huang
  • Lianglong Wang

Abstract

This paper is concerned with stabilization of impulsive stochastic delay differential systems. Based on the Razumikhin techniques and Lyapunov functions, several criteria on pth moment and almost sure exponential stability are established. Our results show that stochastic functional differential systems may be exponentially stabilized by impulses.

Suggested Citation

  • Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Exponential Stability of Impulsive Stochastic Functional Differential Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:678536
    DOI: 10.1155/2012/678536
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/678536
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/678536?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
    ---><---

    References listed on IDEAS

    as
    1. Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Shiguo Peng & Liping Yang, 2010. "Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-11, February.
    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. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    5. 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.
    6. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    7. Zhanhua Yu, 2011. "Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    8. J. Diblík & A. Zafer, 2011. "On Stability of Linear Delay Differential Equations under Perron's Condition," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-9, April.
    9. J. Diblík & A. Zafer, 2011. "On Stability of Linear Delay Differential Equations under Perron′s Condition," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    10. Zhanhua Yu, 2011. "Almost Surely Asymptotic Stability of Exact and Numerical Solutions for Neutral Stochastic Pantograph Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, August.
    11. Sakthivel, R. & Luo, J., 2009. "Asymptotic stability of nonlinear impulsive stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1219-1223, May.
    12. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, May.
    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. Zheng Wu & Hao Huang & Lianglong Wang, 2013. "Stochastic Delay Population Dynamics under Regime Switching: Permanence and Asymptotic Estimation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Zheng Wu & Hao Huang & Lianglong Wang, 2013. "Stochastic Delay Population Dynamics under Regime Switching: Global Solutions and Extinction," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Pei Cheng & Fengqi Yao & Mingang Hua, 2014. "Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.

    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. Zheng Wu & Hao Huang & Lianglong Wang, 2012. "Stochastic Delay Logistic Model under Regime Switching," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    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. 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.
    4. Yao, Fengqi & Deng, Feiqi, 2012. "Exponential stability in terms of two measures of impulsive stochastic functional differential systems via comparison principle," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1151-1159.
    5. L. J. Shen & J. T. Sun, 2011. "Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    6. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    7. Yuanfu Shao & Peiluan Li & Guoqiang Tang, 2012. "Dynamic Analysis of an Impulsive Predator‐Prey Model with Disease in Prey and Ivlev‐Type Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Xuhui Bu & Fashan Yu & Ziyi Fu & Fuzhong Wang, 2013. "Stability Analysis of High‐Order Iterative Learning Control for a Class of Nonlinear Switched Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    9. 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.
    10. X. J. Wan & Y. P. Zhang & J. T. Sun, 2013. "Controllability of Impulsive Neutral Functional Differential Inclusions in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    11. Manlika Rajchakit & Grienggrai Rajchakit, 2012. "Mean Square Exponential Stability of Stochastic Switched System with Interval Time‐Varying Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. Yuanfu Shao & Changjin Xu & Qianhong Zhang, 2012. "Globally Exponential Stability of Periodic Solutions to Impulsive Neural Networks with Time‐Varying Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    13. 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.
    14. Shuping He & Fei Liu, 2012. "Adaptive Observer‐Based Fault Estimation for Stochastic Markovian Jumping Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    15. Ting Cai & Pei Cheng, 2021. "Stability Analysis of Discrete-Time Stochastic Delay Systems with Impulses," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    16. Pei Cheng & Zheng Wu & Lianglong Wang, 2012. "New Results on Global Exponential Stability of Impulsive Functional Differential Systems with Delayed Impulses," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    17. Samidurai, Rajendran & Manivannan, Raman, 2015. "Robust passivity analysis for stochastic impulsive neural networks with leakage and additive time-varying delay components," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 743-762.
    18. Liu, Jinhai & Su, Hanguang & Ma, Yanjuan & Wang, Gang & Wang, Yuan & Zhang, Kun, 2016. "Chaos characteristics and least squares support vector machines based online pipeline small leakages detection," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 656-669.
    19. Chen, Hao & Sun, Jitao, 2012. "Stability analysis for coupled systems with time delay on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 528-534.
    20. Ruofeng Rao & Zhilin Pu, 2013. "LMI‐Based Stability Criterion of Impulsive T‐S Fuzzy Dynamic Equations via Fixed Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnlaaa:v:2012:y:2012:i:1:n:678536. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    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.