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<p>For Takagi-Sugeno (T-S) fuzzy system with time delay, the conservativeness of the existing results mainly stems from the integral inequality and membership functions (MFs). If the integral inequality is hard to be further improved, better results can be obtained by fully utilizing the MFs. In this paper, a MFs-dependent asymmetric Lyapunov-Krasovskii functional (LKF) is constructed, incorporating the MFs extreme value method and allowing the trajectory of the MFs to be represented by its extreme value. Then, the checking points are used to get new stability conditions. Furthermore, the operation interval of the MFs is divided into sub-regions to further reduce the conservativeness. Finally, three examples demonstrate this method’s effectiveness.</p>

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Stability and stabilization for T-S fuzzy systems with time delay by applying extreme value of membership functions

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Pan Yang,
  • Likui Wang,
  • Hak-Keung Lam

摘要

For Takagi-Sugeno (T-S) fuzzy system with time delay, the conservativeness of the existing results mainly stems from the integral inequality and membership functions (MFs). If the integral inequality is hard to be further improved, better results can be obtained by fully utilizing the MFs. In this paper, a MFs-dependent asymmetric Lyapunov-Krasovskii functional (LKF) is constructed, incorporating the MFs extreme value method and allowing the trajectory of the MFs to be represented by its extreme value. Then, the checking points are used to get new stability conditions. Furthermore, the operation interval of the MFs is divided into sub-regions to further reduce the conservativeness. Finally, three examples demonstrate this method’s effectiveness.