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Stability and Stabilization of Impulsive Stochastic Delay Differential Equations

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  • Kaining Wu
  • Xiaohua Ding

Abstract

We consider the stability and stabilization of impulsive stochastic delay differential equations (ISDDEs). Using the Lyapunov-Razumikhin method, we obtain the sufficient conditions to guarantee the p th moment exponential stability of ISDDEs. Then the almost sure exponential stability is considered and the sufficient conditions of the almost sure exponential stability are obtained. Moreover, the stabilization problem of ISDDEs is studied and the criterion on impulsive stabilization of ISDDEs is established. At last, examples are presented to illustrate the correctness of our results.

Suggested Citation

  • Kaining Wu & Xiaohua Ding, 2012. "Stability and Stabilization of Impulsive Stochastic Delay Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-16, May.
    • Handle: RePEc:hin:jnlmpe:176375
    DOI: 10.1155/2012/176375
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    Cited by:

    1. Gui-Lai Zhang & Yang Sun & Ya-Xin Zhang & Chao Liu, 2024. "Euler Method for a Class of Linear Impulsive Neutral Differential Equations," Mathematics, MDPI, vol. 12(18), pages 1-19, September.
    2. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).

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