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H ∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults

Author

Listed:
  • Houssem Jerbi

    (Department of Industrial Engineering, College of Engineering, University of Hail, Hail 2440, Saudi Arabia)

  • Mourad Kchaou

    (Department of Electrical Engineering, College of Engineering, University of Hail, Hail 2440, Saudi Arabia)

  • Attia Boudjemline

    (Department of Industrial Engineering, College of Engineering, University of Hail, Hail 2440, Saudi Arabia)

  • Mohamed Amin Regaieg

    (Lab-STA, LR11ES50, National School of Engineering of Sfax, University of Sfax, Sfax 3038, Tunisia)

  • Sondes Ben Aoun

    (Department of Computer Engineering, College of Computer Science and Engineering, University of Hail, Hail 2440, Saudi Arabia)

  • Ahmed Lakhdar Kouzou

    (Faculty of Electrical and Control Engineering, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233 Gdańsk, Poland)

Abstract

In this paper, the problem of reliable control design with mixed H ∞ /passive performance is discussed for a class of Takagi–Sugeno TS fuzzy descriptor systems with time-varying delay, sensor failure, and randomly occurred non-linearity. Based on the Lyapunov theory, firstly, a less conservative admissible criterion is established by combining the delay decomposition and reciprocally convex approaches. Then, the attention is focused on the design of a reliable static output feedback (SOF) controller with mixed H ∞ /passive performance requirements. The key merit of the paper is to propose a simple method to design such a controller since the system output is subject to probabilistic missing data and noise. Using the output vector as a state component, an augmented model is introduced, and sufficient conditions are derived to achieve the desired performance of the closed-loop system. In addition, the cone complementarity linearization (CCL) algorithm is provided to calculate the controller gains. At last, three numerical examples, including computer-simulated truck-trailer and ball and beam systems are given to show the efficacy of our proposed approach, compared with existing ones in the literature.

Suggested Citation

  • Houssem Jerbi & Mourad Kchaou & Attia Boudjemline & Mohamed Amin Regaieg & Sondes Ben Aoun & Ahmed Lakhdar Kouzou, 2021. "H ∞ and Passive Fuzzy Control for Non-Linear Descriptor Systems with Time-Varying Delay and Sensor Faults," Mathematics, MDPI, vol. 9(18), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2203-:d:631448
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    References listed on IDEAS

    as
    1. Chen, Jian & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2017. "Mixed H∞ and passive control for singular systems with time delay via static output feedback," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 244-253.
    2. Pingjing Yang & Yuechao Ma & Fengman Yang & Debin Kong & Lin Wang, 2018. "Passivity control for uncertain singular discrete T–S fuzzy time-delay systems subject to actuator saturation," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(8), pages 1627-1640, June.
    3. Feng, Zhiguang & Li, Wenxing & Lam, James, 2015. "New admissibility analysis for discrete singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1058-1066.
    4. Liu, Yangfan & Ma, Yuechao & Wang, Yanning, 2018. "Reliable finite-time sliding-mode control for singular time-delay system with sensor faults and randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 341-357.
    5. Qunxian Zheng & Youzhu Ling & Lisheng Wei & Hongbin Zhang, 2018. "Mixed H∞ and passive control for linear switched systems via hybrid control approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(4), pages 818-832, March.
    6. Zheng-Guang Wu & Peng Shi & Hongye Su & Jian Chu, 2012. "Delay-dependent stability analysis for discrete-time singular Markovian jump systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(11), pages 2095-2106.
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    Cited by:

    1. Fenghua Chen & Xinguo Qiu & Khalid A. Alattas & Ardashir Mohammadzadeh & Ebrahim Ghaderpour, 2022. "A New Fuzzy Robust Control for Linear Parameter-Varying Systems," Mathematics, MDPI, vol. 10(18), pages 1-22, September.

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