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On robust set stability and set stabilization of probabilistic Boolean control networks

Author

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  • Wang, Jianjun
  • Liu, Wen
  • Fu, Shihua
  • Xia, Jianwei

Abstract

Under the semi-tensor product method, this paper investigates the robust set stability and robust set stabilization problems for a class of probabilistic Boolean control networks (PBCNs) with disturbances. First, an algorithm to determine the largest robust invariant set (LRIS) of a given set for a PBN with probability one is proposed, and the necessary and sufficient conditions to detect whether the PBN is globally finite-time stable to this invariant set with probability one are established. Second, the PBNs with control inputs are considered, and an algorithm for the largest robust control invariant set (LRCIS) with probability one is provided, based on which, some necessary and sufficient conditions for finite-time robust set stabilization with probability one of PBCNs are presented. Furthermore, the design scheme of time-optimal state feedback stabilizers via antecedence solution technique is derived. The study of illustrative examples shows the effectiveness of the obtained new results.

Suggested Citation

  • Wang, Jianjun & Liu, Wen & Fu, Shihua & Xia, Jianwei, 2022. "On robust set stability and set stabilization of probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    • Handle: RePEc:eee:apmaco:v:422:y:2022:i:c:s0096300322000789
    DOI: 10.1016/j.amc.2022.126992
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    References listed on IDEAS

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    1. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Wang, Jiannan & Guo, Binghui & Wei, Wei & Mi, Zhilong & Yin, Ziqiao & Zheng, Zhiming, 2017. "The stability of Boolean network with transmission sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 70-78.
    3. Wen Liu & Shihua Fu & Jianli Zhao, 2021. "Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    4. Zhang, Qiliang & Feng, Jun-e & Wang, Biao & Wang, Peihe, 2020. "Event-triggered mechanism of designing set stabilization state feedback controller for switched Boolean networks," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    5. Haitao Li & Yuzhen Wang, 2017. "Robust stability and stabilisation of Boolean networks with disturbance inputs," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 750-756, March.
    6. Fu, Shihua & Cheng, Daizhan & Feng, Jun-e & Zhao, Jianli, 2021. "Matrix expression of finite Boolean-type algebras," Applied Mathematics and Computation, Elsevier, vol. 395(C).
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    Cited by:

    1. Chen, Haodong & Li, Lulu & Lu, Jianquan & Alghamdi, Sultan M, 2023. "Asymptotical set stabilization of large-scale logical networks with stochastic delays and the application in finite-field networks," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Li, Xi & Liu, Yang & Lou, Jungang & Lu, Jianquan, 2023. "Robust minimal strong reconstructibility problem of Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 458(C).

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