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Robust stability of Markov jump linear systems through randomized evaluations

Author

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  • Vargas, Alessandro N.
  • Montezuma, Marcio A.F.
  • Liu, Xinghua
  • Oliveira, Ricardo C.L.F.

Abstract

The paper presents a method for checking the robust mean square stability of continuous-time Markov jump linear systems. The robustness arises in the analysis due to the assumption that the Markovian transition probability matrix is partially known. The corresponding infinite-dimensional robust stability problem, difficult to solve, is then converted into a probabilistic problem, amenable to the numerical viewpoint, taking advantage of the randomized (scenario) approach. The paper shows examples—including a real-time electronic-circuit application—for which the results from the literature fail to determine the robust stability but the randomized approach gives a positive answer.

Suggested Citation

  • Vargas, Alessandro N. & Montezuma, Marcio A.F. & Liu, Xinghua & Oliveira, Ricardo C.L.F., 2019. "Robust stability of Markov jump linear systems through randomized evaluations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 287-294.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:287-294
    DOI: 10.1016/j.amc.2018.09.064
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    References listed on IDEAS

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    1. Gao, Xianwen & He, Hangfeng & Qi, Wenhai, 2017. "Admissibility analysis for discrete-time singular Markov jump systems with asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 431-441.
    2. Li-Wei Li & Guang-Hong Yang, 2017. "Fault estimation for a class of nonlinear Markov jump systems with general uncertain transition rates," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 805-817, March.
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    Cited by:

    1. Hamdi, Issam El & Vargas, Alessandro N. & Bouzahir, Hassane & Oliveira, Ricardo C.L.F. & Acho, Leonardo, 2021. "Robust stability of stochastic systems with varying delays: Application to RLC circuit with intermittent closed-loop," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    2. Xu, Qiyi & Zhang, Ning & Qi, Wenhai, 2023. "Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    3. Dai, Mingcheng & Huang, Zhengguo & Xia, Jianwei & Meng, Bo & Wang, Jian & Shen, Hao, 2019. "Non-fragile extended dissipativity-based state feedback control for 2-D Markov jump delayed systems," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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