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Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems

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  • Hyun Kim, Sung

Abstract

This paper is concerned with the robust H∞ filtering problem for continuous-time nonhomogeneous Markovian jump systems via generalized relaxation techniques. To provide more general description on transition rates, this paper first presents four (or five) specific cases that can be classified according to the property of transition rates. And then, two generalized relaxation methods are proposed so that they can embrace all possible cases identified from our classification, even the excluded case from other results. Especially, to develop a less conservative relaxation process with reduced computational complexity, this paper proposes an improved approach that imposes the summation constraint of transition rates without resorting to extra slack variables, and takes advantage of their component-summation-based constraints.

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  • Hyun Kim, Sung, 2019. "Generalized relaxation techniques for robust H∞ filtering of nonhomogeneous Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 542-556.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:542-556
    DOI: 10.1016/j.amc.2018.10.075
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    References listed on IDEAS

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    1. Wang, Guoliang & Li, Zhiqiang & Zhang, Qingling & Yang, Chunyu, 2017. "Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 377-393.
    2. Yang, Guowei & Kao, Yonggui & Jiang, Baoping & Yin, Jile, 2017. "Delay-dependent H∞ filtering for singular Markovian jump systems with general uncomplete transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 195-215.
    3. Shen, Mouquan & Yan, Shen & Zhang, Guangming & Park, Ju H., 2016. "Finite-time H∞ static output control of Markov jump systems with an auxiliary approach," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 553-561.
    4. Ma, Yuechao & Chen, Hui, 2015. "Reliable finite-time H∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 897-915.
    5. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
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    Cited by:

    1. Feng, Zhiguang & Feng, Bo & Zhang, Naifu, 2023. "Fuzzy-based asynchronous controller design on reachable set synthesis of nonlinear hidden Markovian jump systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous H∞ observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates," Applied Mathematics and Computation, Elsevier, vol. 411(C).

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