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    Area of Science:

    • Control Systems Engineering
    • Fuzzy Logic Systems
    • Nonlinear Systems Analysis

    Background:

    • Asynchronous H∞ filtering is crucial for systems with state mismatches and data uncertainties.
    • Discrete-time Takagi-Sugeno fuzzy affine systems are widely used to model complex nonlinear dynamics.
    • Time-varying delays and measurement quantization pose significant challenges to filter design.

    Purpose of the Study:

    • To design an asynchronous H∞ filter for discrete-time Takagi-Sugeno fuzzy affine systems.
    • To address challenges posed by time-varying signal transmission delays and measurement quantization.
    • To ensure asymptotic stability and a prescribed H∞ performance index for the filtering error system.

    Main Methods:

    • Transformation of the filtering error system into an input-output form with interconnected subsystems.
    • Application of the scaled small gain theorem to establish filter existence conditions.
    • Utilization of a novel piecewise Lyapunov-Krasovskii functional and the S-procedure approach.

    Main Results:

    • Sufficient conditions for the existence of the asynchronous H∞ filter are derived.
    • The proposed filter guarantees asymptotic stability of the closed-loop system.
    • The filter achieves a prescribed H∞ performance index, accommodating adjustable quantization density.

    Conclusions:

    • The developed asynchronous H∞ filter effectively handles time-varying delays and quantization in Takagi-Sugeno fuzzy affine systems.
    • The theoretical results are validated through a practical cart-pendulum example.
    • The methodology provides a robust framework for designing filters in complex, uncertain systems.