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<p>The main objective of this paper is to present a novel control strategy to deal with the stabilization of Takagi–Sugeno (T–S) fuzzy system with time-varying delays. Time delays can induce oscillatory responses or even lead to system divergence, thereby posing a significant threat to the stability of dynamic systems. To address this issue, a T–S fuzzy observer is created to reconstruct the system’s states that are not directly measurable. Its design is therefore based on the parallel distributed compensation (PDC) method, which facilitates the construction of a fuzzy functional observer for controller synthesis. Moreover, its application also allows the estimation of the state functions employed in the PDC-based controller for system stabilization. For all of this, closed-loop stability conditions are established using Lyapunov–Krasovskii functionals and expressed as Linear Matrix Inequalities (LMIs) that can be numerically optimized. The resulting LMIs allow for the direct computation of both the observer and controller gain matrices. Finally, numerical simulations and physical application are conducted to evaluate the performance and the effectiveness of the proposed approach. The results demonstrate a significant improvement in the system’s stability and performance.</p>

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A Novel Functional Observer-Based Control Approach for Takagi–Sugeno (T–S) Fuzzy Systems with Time-Varying Delays

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Salma El Azzouzi,
  • Omar El Aazzaoui,
  • Amina El Maach,
  • Mohamed Ouahi,
  • Mohammed Charqi

摘要

The main objective of this paper is to present a novel control strategy to deal with the stabilization of Takagi–Sugeno (T–S) fuzzy system with time-varying delays. Time delays can induce oscillatory responses or even lead to system divergence, thereby posing a significant threat to the stability of dynamic systems. To address this issue, a T–S fuzzy observer is created to reconstruct the system’s states that are not directly measurable. Its design is therefore based on the parallel distributed compensation (PDC) method, which facilitates the construction of a fuzzy functional observer for controller synthesis. Moreover, its application also allows the estimation of the state functions employed in the PDC-based controller for system stabilization. For all of this, closed-loop stability conditions are established using Lyapunov–Krasovskii functionals and expressed as Linear Matrix Inequalities (LMIs) that can be numerically optimized. The resulting LMIs allow for the direct computation of both the observer and controller gain matrices. Finally, numerical simulations and physical application are conducted to evaluate the performance and the effectiveness of the proposed approach. The results demonstrate a significant improvement in the system’s stability and performance.