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Stability and Stabilization of Impulsive Stochastic Delay Difference Equations

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  • Kaining Wu
  • Xiaohua Ding
  • Liming Wang

Abstract

When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS is stable, then what kind of impulse can the original system tolerate to keep stable? If the SDDS is unstable, then what kind of impulsive strategy should be taken to make the system stable? Using the Lyapunov-Razumikhin technique, we establish criteria for the stability of impulsive stochastic delay difference equations and these criteria answer those questions. As for applications, we consider a kind of impulsive stochastic delay difference equation and present some corollaries to our main results.

Suggested Citation

  • Kaining Wu & Xiaohua Ding & Liming Wang, 2010. "Stability and Stabilization of Impulsive Stochastic Delay Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-15, March.
    • Handle: RePEc:hin:jnddns:592036
    DOI: 10.1155/2010/592036
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    Cited by:

    1. 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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