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    Area of Science:

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

    Background:

    • Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling nonlinear systems.
    • Variable sampling control introduces challenges in ensuring system stability and performance.
    • Dissipative stability is crucial for robust control system design.

    Purpose of the Study:

    • To design a sampled-data controller for T-S fuzzy systems with constant time delays.
    • To achieve global asymptotic stability with a specified (Q,S,R) - γ -dissipative performance index.
    • To determine the maximal-allowable upper bound (MAUB) for sampling periods.

    Main Methods:

    • Utilizing a novel piecewise Lyapunov-Krasovskii functional (LKF).
    • Employing a looped-functional and free-matrix-based (FMB) inequality method.
    • Deriving linear matrix inequality (LMI) conditions for stability analysis and controller design.

    Main Results:

    • Established LMI conditions to verify the dissipative stability of T-S fuzzy systems.
    • Derived controller gains matrices using the LMI approach.
    • Determined the MAUB of sampling periods for stability.

    Conclusions:

    • The proposed method effectively designs controllers for stable and dissipative T-S fuzzy systems under variable sampling.
    • The LMI conditions are computationally tractable using standard MATLAB toolboxes.
    • A truck-trailer system example demonstrates the effectiveness and superiority of the proposed scheme.