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Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems

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  • Feng, Lichao
  • Liu, Lei
  • Wu, Zhihui
  • Liu, Qiumei

Abstract

Recently, the asymptotic stability for Markov jump stochastic functional differential systems (SFDSs) was studied, whose stability criteria relied on the intervals lengths of continuous delays. Whereas, so far all the existing references require the rigorous global Lipschitz condition for the delay parts of the drift coefficients and do not consider the challenging factors of exponential decay and neutral issue. Motivated by the aforementioned considerations and the advantages of the degenerate functionals, this paper aims to weaken the global Lipschitz condition for the delay parts of the drift coefficients and investigate the delay-dependent exponential stability and asymptotic boundedness for highly nonlinear Markov jump neutral SFDSs with the method of multiple degenerate functionals. Of course, the delay-independent assertions are as well derived here.

Suggested Citation

  • Feng, Lichao & Liu, Lei & Wu, Zhihui & Liu, Qiumei, 2021. "Stability analysis for nonlinear Markov jump neutral stochastic functional differential systems," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    • Handle: RePEc:eee:apmaco:v:394:y:2021:i:c:s0096300320307359
    DOI: 10.1016/j.amc.2020.125782
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    References listed on IDEAS

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    1. Wu, Fuke & Hu, Shigeng, 2011. "Khasminskii-type theorems for stochastic functional differential equations with infinite delay," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1690-1694, November.
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    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. Wang, Pengfei & Zou, Wenqing & Su, Huan, 2019. "Stability of complex-valued impulsive stochastic functional differential equations on networks with Markovian switching," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 338-354.
    5. Ruan, Dehao & Xu, Liping & Luo, Jiaowan, 2019. "Stability of hybrid stochastic functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 832-841.
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    Cited by:

    1. Liu, Jiamin & Li, Zhao-Yan & Deng, Feiqi, 2021. "Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Song, Gongfei & Zhang, Zimeng & Zhu, Yanan & Li, Tao, 2022. "Discrete-time control for highly nonlinear neutral stochastic delay systems," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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