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    This study introduces a dual event-triggered (DET) mechanism and polynomial dynamic output-feedback (PDOF) controller for positive polynomial fuzzy systems (PPFSs). An improved genetic algorithm (IGA) expands the trigger range and reduces frequencies, enhancing system performance.

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    Area of Science:

    • Control Systems Engineering
    • Fuzzy Systems Theory
    • Nonlinear Control

    Background:

    • Positive polynomial fuzzy systems (PPFSs) present unique challenges in control design due to inherent positivity constraints.
    • Uncertainty and disturbance constraints necessitate robust control strategies for PPFSs.
    • Event-triggered control mechanisms offer potential for reduced communication and computational load.

    Purpose of the Study:

    • To co-design a dual event-triggered (DET) mechanism and a polynomial dynamic output-feedback (PDOF) controller for uncertain PPFSs.
    • To ensure $L_{1}$-gain performance and strict positivity under disturbance constraints.
    • To overcome the conservativeness of existing methods by expanding the admissible DET threshold range.

    Main Methods:

    • A 1-norm DET mechanism is proposed to asynchronously update measurement outputs and PDOF control signals, ensuring compatibility with PPFS positivity.
    • Auxiliary variables and constraints are introduced to derive sufficient conditions for the DET-PDOF controller solution.
    • A multivariate optimization method based on an improved genetic algorithm (IGA) is developed to optimize the DET threshold and controller variables.

    Main Results:

    • Sufficient conditions for the existence of the DET-PDOF controller are established, guaranteeing $L_{1}$-gain performance and strict positivity.
    • The proposed IGA-based method effectively expands the admissible DET threshold range, mitigating conservativeness.
    • The approach demonstrates significant suppression of dual-triggering frequencies, leading to improved transmission performance.

    Conclusions:

    • The co-design of DET mechanism and PDOF controller is feasible for uncertain PPFSs, ensuring stability and performance.
    • The IGA-based optimization significantly enhances the applicability and efficiency of event-triggered control for PPFSs.
    • Validation through numerical and practical examples confirms the effectiveness of the proposed control scheme.