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Stabilization in general decay rate of discrete feedback control for non-autonomous Markov jump stochastic systems

Author

Listed:
  • Feng, Lichao
  • Liu, Qiumei
  • Cao, Jinde
  • Zhang, Chunyan
  • Alsaadi, Fawaz

Abstract

For an unstable Markov jump stochastic differential system (MJ-SDS) with high nonlinearity, can one introduce a discrete feedback control to stabilize it? This question has been well answered for the case of the feedback control derived from discrete state observations, in the form of H∞ stabilization and exponential stabilization. Whereas, the existing theory can not tackle the non-autonomous systems and do not consider the factor of discrete mode observations, which are the motivations of this paper. Fortunately, for an unstable non-autonomous MJ-SDS, the feedback control, originated from discrete observations of system state and system mode, is well designed to stabilize it not only in the sense of exponential decay rate but also of polynomial decay rate and even general decay rate. Thereinto, the designing rule of discrete feedback control is given as well.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:417:y:2022:i:c:s0096300321008535
    DOI: 10.1016/j.amc.2021.126771
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    References listed on IDEAS

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    1. Li, Bing, 2017. "A note on stability of hybrid stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 45-57.
    2. 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).
    3. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    4. You, Surong & Hu, Liangjian & Mao, Wei & Mao, Xuerong, 2015. "Robustly exponential stabilization of hybrid uncertain systems by feedback controls based on discrete-time observations," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 8-16.
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    Cited by:

    1. 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).

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