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Stability of Markovian jump stochastic parabolic Itô equations with generally uncertain transition rates

Author

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  • Zhang, Caihong
  • Kao, Yonggui
  • Kao, Binghua
  • Zhang, Tiezhu

Abstract

In this paper, the stability problem for delayed Markovian jump stochastic parabolic Ito^ equations (DMJSPIEs) subject to generally uncertain transition rates (GUTRs) is investigated via Lyapunov-Krasovskii functional and linear matrix inequality (LMI) method. In the model discussed, we suppose that only part of the transition rates of the jumping process are known, namely, some factors have been already available, some elements have been simply known with lower and upper bounds, and the rest of elements may have no useful information. Lastly, the applicability and effectiveness of the obtained results are illustrated through an example.

Suggested Citation

  • Zhang, Caihong & Kao, Yonggui & Kao, Binghua & Zhang, Tiezhu, 2018. "Stability of Markovian jump stochastic parabolic Itô equations with generally uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 399-407.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:399-407
    DOI: 10.1016/j.amc.2018.04.050
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    References listed on IDEAS

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    1. Yonggui Kao & Hamid Reza Karimi, 2014. "Stability in Mean of Partial Variables for Coupled Stochastic Reaction-Diffusion Systems on Networks: A Graph Approach," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, May.
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    Cited by:

    1. Suriguga, Ma & Kao, Yonggui & Hyder, Abd-Allah, 2020. "Uniform stability of delayed impulsive reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    2. Han, Xin-Xin & Wu, Kai-Ning & Ding, Xiaohua, 2020. "Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control," Applied Mathematics and Computation, Elsevier, vol. 385(C).

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