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Asynchronous H∞ observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates

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  • Nguyen, Ngoc Hoai An
  • Kim, Sung Hyun

Abstract

This paper deals with the problem of asynchronous H∞ observer-based control for continuous-time nonhomogeneous Markovian jump systems with generalized incomplete transition rates. Different from other existing papers, the effects of both nonhomogeneity and asynchronism on observer-based control design are discussed in detail to address more realistic phenomena. Furthermore, to decouple the Lyapunov matrix from the control gain while improving the control performance, this paper proposes a state extension method as an alternative to the conventional separation method. Not only that, to derive a set of LMI-based stabilization conditions, this paper presents a less conservative relaxation technique that reduces its computational burden. Finally, two illustrative examples are provided to show the validity of the proposed method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:411:y:2021:i:c:s0096300321006160
    DOI: 10.1016/j.amc.2021.126532
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    References listed on IDEAS

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    1. Yun Chen & Zhangping Chen & Zhenyu Chen & Anke Xue, 2020. "Observer-based passive control of non-homogeneous Markov jump systems with random communication delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(6), pages 1133-1147, April.
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    3. Yu, Peng & Ma, Yuechao, 2020. "Observer-based asynchronous control for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    5. Wu, Yuyan & Cheng, Jun & Zhou, Xia & Cao, Jinde & Luo, Mengzhuo, 2021. "Asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
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    7. Li, Min & Liu, Ming & Zhang, Yingchun, 2020. "Asynchronous adaptive dynamic output feedback sliding mode control for singular markovian jump systems with actuator faults and uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    8. Xu, Zhaowen & Su, Hongye & Shi, Peng & Wu, Zheng-Guang, 2019. "Asynchronous H∞ control of semi-Markov jump linear systems," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 270-280.
    9. Jin Zhu & Pengfei Jiang, 2020. "Mean stability for a class of discrete-time non-homogeneous positive Markov jump linear systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(16), pages 3163-3178, December.
    10. Cai, Xiao & Zhong, Shouming & Wang, Jun & Shi, Kaibo, 2020. "Robust H∞ control for uncertain delayed T-S fuzzy systems with stochastic packet dropouts," Applied Mathematics and Computation, Elsevier, vol. 385(C).
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    Cited by:

    1. Lee, Won Il & Park, Bum Yong & Kim, Sung Hyun, 2022. "Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    2. Anh Tuan Vo & Thanh Nguyen Truong & Hee-Jun Kang, 2023. "Fixed-Time RBFNN-Based Prescribed Performance Control for Robot Manipulators: Achieving Global Convergence and Control Performance Improvement," Mathematics, MDPI, vol. 11(10), pages 1-25, May.
    3. Khanh Hieu Nguyen & Sung Hyun Kim, 2022. "Event-Triggered Non-PDC Filter Design of Fuzzy Markovian Jump Systems under Mismatch Phenomena," Mathematics, MDPI, vol. 10(16), pages 1-25, August.

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