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Exponential Stability of Impulsive Stochastic Delay Differential Systems

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  • Xiaotai Wu
  • Litan Yan
  • Wenbing Zhang
  • Liang Chen

Abstract

This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the th moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.

Suggested Citation

  • Xiaotai Wu & Litan Yan & Wenbing Zhang & Liang Chen, 2012. "Exponential Stability of Impulsive Stochastic Delay Differential Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-15, January.
    • Handle: RePEc:hin:jnddns:296136
    DOI: 10.1155/2012/296136
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    Cited by:

    1. Chunxiang Li & Fangshu Hui & Fangfei Li, 2023. "Stability of Differential Systems with Impulsive Effects," Mathematics, MDPI, vol. 11(20), pages 1-23, October.
    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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