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Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control

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  • Han, Xin-Xin
  • Wu, Kai-Ning
  • Ding, Xiaohua

Abstract

This paper investigates the finite-time stability (FTS) for a class of stochastic Markovian reaction-diffusion systems (SMRDSs). First, a boundary control strategy is put forward. Under the designed boundary controller, a sufficient condition of FTS for SMRDSs is provided based on the method of Lyapunov-Krasovskii functional combined with inequality techniques.When there exists the incompleteness of transition rate information, we further study the problem of SMRDSs with partially unknown transition rates (TRs) by adding a set of symmetric free matrices. An FTS criterion is also obtained for this case. Theoretical results show that the case of completely known TRs is the special case of partially unknown TRs. Finally, simulation examples are presented to verify the validity of our derived results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303830
    DOI: 10.1016/j.amc.2020.125422
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    References listed on IDEAS

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    1. Wu, Kai-Ning & Sun, Han-Xiao & Yang, Baoqing & Lim, Cheng-Chew, 2018. "Finite-time boundary control for delay reaction–diffusion systems," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 52-63.
    2. 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.
    3. Wang, Aijuan & Liao, Xiaofeng & Dong, Tao, 2018. "Finite-time event-triggered synchronization for reaction–diffusion complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 111-120.
    4. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    5. M. Syed Ali & J. Yogambigai & O. M. Kwon, 2018. "Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 718-735, March.
    6. Xiao-Zhen Liu & Kai-Ning Wu & Weihai Zhang, 2019. "Mean square finite-time boundary stabilisation and H∞ boundary control for stochastic reaction-diffusion systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 50(7), pages 1388-1398, May.
    7. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Jian & Wang, Zhen, 2019. "Passive state estimation for fuzzy jumping neural networks with fading channels based on the hidden Markov model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
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    Cited by:

    1. Cheng Peng & Jiaxin Ma & Qiankun Li & Shang Gao, 2022. "Noise-to-State Stability in Probability for Random Complex Dynamical Systems on Networks," Mathematics, MDPI, vol. 10(12), pages 1-11, June.
    2. Zou, Cong & Li, Bing & Liu, Feiyang & Xu, Bingrui, 2022. "Event-Triggered μ-state estimation for Markovian jumping neural networks with mixed time-delays," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Li, Xing-Yu & Wu, Kai-Ning & Liu, Xiao-Zhen, 2023. "Mittag–Leffler stabilization for short memory fractional reaction-diffusion systems via intermittent boundary control," Applied Mathematics and Computation, Elsevier, vol. 449(C).

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