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A traverse algorithm approach to stochastic stability analysis of Markovian jump systems with unknown and uncertain transition rates

Author

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  • Jiang, Baoping
  • Wu, Zhengtian
  • Karimi, Hamid Reza

Abstract

This paper intents to investigate the problem of mean-square stability analysis of Markovian jump systems with generally unknown and uncertain transition rates. Different from pervious works that the transition rates from one mode to others may be partially unknown or uncertain, in this note, the case that the transition rates from one mode to others are totally unknown will be investigated. By means of transition rate estimation, two ways are provided to tackle with the totally unknown case. In general, five cases in the transition rates matrix are studied for the mean-square stability analysis, which almost have covered all types of generally unknown and uncertain transition rates. Simultaneously, corresponding conditions for checking the mean-square stability of the considered Markovian jump systems are developed for the five studied cases. Finally, numerical examples are provided to verify the effectiveness of the proposed results.

Suggested Citation

  • Jiang, Baoping & Wu, Zhengtian & Karimi, Hamid Reza, 2022. "A traverse algorithm approach to stochastic stability analysis of Markovian jump systems with unknown and uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000546
    DOI: 10.1016/j.amc.2022.126968
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    References listed on IDEAS

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    1. Feng, Lichao & Liu, Qiumei & Cao, Jinde & Zhang, Chunyan & Alsaadi, Fawaz, 2022. "Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems," Applied Mathematics and Computation, Elsevier, vol. 417(C).
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    Cited by:

    1. Sub Lee, Ho & Park, Chan-eun & Park, PooGyeon, 2024. "A search algorithm for the compact uncertainty region of system elements with interval and affine constraint properties," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    2. Li, Jiayang & Zhang, Zhikun & Dai, Min & Ming, Ju & Wang, Xiangjun, 2023. "Diffusion equations with Markovian switching: Well-posedness, numerical generation and parameter inference," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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