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Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme

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  • Lee, Won Il
  • Park, Bum Yong
  • Kim, Sung Hyun

Abstract

This paper aims to design a robust observer-based dissipative controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems with nonhomogeneous Markov jumps through a non-parallel distributed compensation (non-PDC) scheme. Based on a mode-dependent nonquadratic Lyapunov function, the final form of the stabilization conditions is expressed as linear matrix inequalities in a less conservative manner. To be specific, this paper proposes a decoupling technique that can address the inherent nonconvex terms by extracting them from the stabilization conditions, where all slack variables are set to be fuzzy-basis-dependent for less conservative performance. Furthermore, the proposed stabilization method adopts a one-step design strategy that simultaneously designs the fuzzy observer and control gains without any iteration procedures by employing a positive tuning parameter. In particular, the time-varying transition probabilities included in the stabilization conditions are effectively removed using a modified relaxation technique that can avoid excessive use of free weighting matrices. Finally, based on four examples, the validity of the proposed method is verified through comparison with other studies.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s009630032200529x
    DOI: 10.1016/j.amc.2022.127455
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    References listed on IDEAS

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    1. Shu, Feng & Li, Min & Liu, Duyu, 2019. "Non-fragile H∞ control for Markovian jump fuzzy systems with time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1177-1191.
    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).
    3. Gao, Meng & Zhang, Lihua & Qi, Wenhai & Cao, Jinde & Cheng, Jun & Kao, Yonggui & Wei, Yunliang & Yan, Xiaoyu, 2020. "SMC for semi-Markov jump T-S fuzzy systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    4. Liang, Xingyue & Xia, Jianwei & Chen, Guoliang & Zhang, Huasheng & Wang, Zhen, 2019. "Dissipativity-based sampled-data control for fuzzy Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 552-564.
    5. Wang, Yanqian & Chen, Fu & Zhuang, Guangming & Yang, Guang, 2020. "Dynamic event-based mixed H∞ and dissipative asynchronous control for Markov jump singularly perturbed systems," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    6. Xu, Tianshu & Xia, Jianwei & Wang, Sanxia & Lian, Yuxiao & Zhang, Huasheng, 2020. "Extended dissipativity-based non-fragile sampled-data control of fuzzy Markovian jump systems with incomplete transition rates," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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    Cited by:

    1. Thanh Binh Nguyen & Hyoung-Kyu Song, 2022. "Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties," Mathematics, MDPI, vol. 10(19), pages 1-16, October.

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