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Improved stabilization condition of delayed T-S fuzzy systems via an extended quadratic function negative-determination lemma

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  • Yang, Tianqing
  • Zou, Runmin
  • Liu, Fang
  • Liu, Cai
  • Sidorov, Denis

Abstract

This paper focuses on the stability and stabilization problems of continuous-time T-S fuzzy systems (TSFS) with variable delay. A new augmented Lyapunov–Krasovskii functional (LKF) is established by combining the negative quadratic term with the alterable delay-product-integral term. To further improve the results, an extended quadratic function negative-determination (QFND) lemma is proposed to deal with δ(t)-related quadratic function in the LKF derivative. Subsequently, based on the parallel distributed compensation (PDC) technique, a bounded delay correlation stabilization criterion is derived. Finally, the proposed methods are applied to a numerical example and an inverted pendulum system to verify their effectiveness and superiority.

Suggested Citation

  • Yang, Tianqing & Zou, Runmin & Liu, Fang & Liu, Cai & Sidorov, Denis, 2023. "Improved stabilization condition of delayed T-S fuzzy systems via an extended quadratic function negative-determination lemma," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923009566
    DOI: 10.1016/j.chaos.2023.114055
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    References listed on IDEAS

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    1. Vadivel, R. & Sabarathinam, S. & Wu, Yongbao & Chaisena, Kantapon & Gunasekaran, Nallappan, 2022. "New results on T–S fuzzy sampled-data stabilization for switched chaotic systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    3. Saravanakumar, Ramasamy & Datta, Rupak & Cao, Yang, 2022. "New insights on fuzzy sampled-data stabilization of delayed nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
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    1. Pessim, Paulo S.P. & Coutinho, Pedro Henrique Silva & Lacerda, Márcio J. & Palhares, Reinaldo Martínez, 2023. "Distributed event-triggered fuzzy control for nonlinear interconnected systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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