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Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function

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  • Xiaoyan Liu
  • Quanxin Zhu

Abstract

This paper deals with stochastically globally exponential stability (SGES) for stochastic impulsive differential systems (SIDSs) with discrete delays (DDs) and infinite distributed delays (IDDs). By using vector Lyapunov function (VLF) and average dwell-time (ADT) condition, we investigate the unstable impulsive dynamics and stable impulsive dynamics of the suggested system, and some novel stability criteria are obtained for SIDSs with DDs and IDDs. Moreover, our results allow the discrete delay term to be coupled with the nondelay term, and the infinite distributed delay term to be coupled with the nondelay term. Finally, two examples are given to verify the effectiveness of our theories.

Suggested Citation

  • Xiaoyan Liu & Quanxin Zhu, 2020. "Stochastically Globally Exponential Stability of Stochastic Impulsive Differential Systems with Discrete and Infinite Distributed Delays Based on Vector Lyapunov Function," Complexity, Hindawi, vol. 2020, pages 1-16, December.
    • Handle: RePEc:hin:complx:7913050
    DOI: 10.1155/2020/7913050
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    Cited by:

    1. Aadhithiyan, S. & Raja, R. & Zhu, Q. & Alzabut, J. & Niezabitowski, M. & Lim, C.P., 2021. "Modified projective synchronization of distributive fractional order complex dynamic networks with model uncertainty via adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Thoiyab, N. Mohamed & Muruganantham, P. & Zhu, Quanxin & Gunasekaran, Nallappan, 2021. "Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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