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Stability and stabilization analysis of T-S fuzzy systems with distributed time-delay using state-feedback control

Author

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  • Bhuvaneshwari, G.
  • Prakash, M.
  • Rakkiyappan, R.
  • Manivannan, A.

Abstract

In this study, a stability and stabilization analysis is discussed for Takagi–Sugeno (T-S) fuzzy systems with distributed time-delays. A fuzzy-based memory state-feedback control is designed to stabilize the delayed T-S fuzzy systems. A new Lyapunov–Krasovskii functional is constructed in an augmented form with information about the lower and upper bounds. Based on this functional, asymptotic stability of the closed-loop T-S fuzzy systems is achieved, and sufficient conditions are derived in linear matrix inequality form. In the numerical example section, comparative results are given with their simulation results to show the merits of the proposed approach and control scheme.

Suggested Citation

  • Bhuvaneshwari, G. & Prakash, M. & Rakkiyappan, R. & Manivannan, A., 2023. "Stability and stabilization analysis of T-S fuzzy systems with distributed time-delay using state-feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 778-793.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:778-793
    DOI: 10.1016/j.matcom.2022.10.004
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    References listed on IDEAS

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    1. Li, Min & Shu, Feng & Liu, Duyu & Zhong, Shouming, 2018. "Robust H∞ control of T-S fuzzy systems with input time-varying delays: A delay partitioning method," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 209-222.
    2. Mingchu Xu & Zhen Xu, 2020. "Stabilisation of T-S fuzzy systems with mixed time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(10), pages 1814-1824, July.
    3. Yongsheng Ma & Mouquan Shen & Haiping Du & Yuesheng Ren & Guangrui Bian, 2020. "An iterative observer-based fault estimation for discrete-time T-S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(6), pages 1007-1018, April.
    4. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    5. Senouci, Abdelkader & Boukabou, Abdelkrim, 2014. "Predictive control and synchronization of chaotic and hyperchaotic systems based on a T–S fuzzy model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 62-78.
    6. Min Li & Ming Liu & Yingchun Zhang & Yunhai Geng, 2018. "Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(7), pages 1353-1367, May.
    7. Yanhui Li & Yulong Li, 2017. "Robust output tracking control for uncertain networked control systems described by T-S fuzzy model with distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(15), pages 3296-3304, November.
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    Cited by:

    1. Yassine Benyazid & Mohamed Fnadi & Ahmed Said Nouri, 2023. "A Discrete Integral Sliding Manifold for a Nonlinear System with Time Delay: An Event-Triggered Scheme," Mathematics, MDPI, vol. 11(10), pages 1-19, May.

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