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    This study introduces event-triggered decentralized asynchronous (ETDA) control for positive interconnected switched systems (PISSs). The novel approach ensures system stability under mode-dependent minimum dwell-time constraints using a linear programming method.

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    Area of Science:

    • Control Systems Engineering
    • Systems Theory
    • Optimization Theory

    Background:

    • Positive interconnected switched systems (PISSs) present unique control challenges due to their inherent positivity and switching dynamics.
    • Decentralized control strategies are crucial for large-scale systems, but achieving asynchronous control under event-triggering adds complexity.
    • Mode-dependent minimum dwell-time (MDMDT) constraints are essential for ensuring stability in switched systems but complicate controller design.

    Purpose of the Study:

    • To design a novel event-triggered decentralized asynchronous (ETDA) control framework for positive interconnected switched systems (PISSs).
    • To address the challenge of mode-dependent minimum dwell-time (MDMDT) constraints within the ETDA control design.
    • To develop a feasible and tractable control scheme using linear programming (LP).

    Main Methods:

    • Development of a 1-norm-based event-triggered mechanism (ETM) and a decentralized asynchronous control strategy (DACS).
    • Construction of a discretized linear copositive Lyapunov function (DLCLF) tailored for MDMDT switching.
    • Application of matrix decomposition for ETDA controller gains and a linear programming (LP) approach for controller synthesis.

    Main Results:

    • A sufficient positivity criterion for closed-loop PISSs was established.
    • A feasible mode-dependent ETDA control scheme was presented using a tractable LP approach.
    • The proposed ETDA control scheme demonstrated the capability to encompass event-triggered decentralized synchronous (ETDS), time-triggered decentralized asynchronous (TTDA), and time-triggered decentralized synchronous (TTDS) control as special cases.

    Conclusions:

    • The designed ETDA control scheme effectively manages PISSs under MDMDT constraints.
    • The proposed methodology offers a unified framework that can be specialized for various control scenarios (event-triggered/time-triggered, asynchronous/synchronous).
    • Comparisons confirm the significance and feasibility of the developed control strategy for practical applications.