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Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties

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  • Thanh Binh Nguyen

    (Department of Information and Communication Engineering and Convergence Engineering for Intelligent Drone, Sejong University, Seoul 05006, Korea)

  • Hyoung-Kyu Song

    (Department of Information and Communication Engineering and Convergence Engineering for Intelligent Drone, Sejong University, Seoul 05006, Korea)

Abstract

This paper investigates an improved criterion to synthesize dissipative observer-based controllers for Markovian jump fuzzy systems under model uncertainties. Since fuzzy-basis functions include some immeasurable state variable or uncertain parameters, there are differences in the fuzzy-basis functions between controller and plant, which is a mismatched phenomenon. This work presents the first attempt for applying double-fuzzy summation-based Lyapunov functions for the observer-based control scheme of the Markov jump fuzzy system regarding the mismatched phenomenon. To be specific, the dissipative conditions are formulated in terms of uncertain parameterized bilinear matrix inequalities. Based on the improved relaxation techniques, a linear-matrix-inequality (LMI)-based algorithm is proposed in the framework of sequence linear programming matrix method. The obtained observer-based controller ensures that the closed-loop system is stochastically stable, and the dissipative performances produce less conservative results compared to preceding works via two numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3620-:d:932676
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    References listed on IDEAS

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    1. Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    2. S. Xu & T. Chen & J. Lam, 2004. "Robust H ∞ Filtering for a Class of Nonlinear Discrete-Time Markovian Jump Systems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 651-668, September.
    3. B. El Haiek & A. Hmamed & A. El Hajjaji & E.H. Tissir, 2017. "Improved results on observer-based control for discrete-time fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(12), pages 2544-2553, September.
    4. 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).
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    Cited by:

    1. Aravindh Dharmarajan & Parivallal Arumugam & Sakthivel Ramalingam & Kavikumar Ramasamy, 2023. "Equivalent-Input-Disturbance Based Robust Control Design for Fuzzy Semi-Markovian Jump Systems via the Proportional-Integral Observer Approach," Mathematics, MDPI, vol. 11(11), pages 1-16, June.
    2. Shuxia Jing & Chengming Lu & Zhimin Li, 2024. "Dissipative Fuzzy Filtering for Nonlinear Networked Systems with Dynamic Quantization and Data Packet Dropouts," Mathematics, MDPI, vol. 12(2), pages 1-17, January.

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