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Fixed/Preassigned-Time Synchronization of Complex Networks via Improving Fixed-Time Stability.

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    This study enhances fixed-time (FXT) and preassigned-time (PAT) synchronization for discontinuous dynamic networks. New methods achieve faster settling times and prespecified synchronization, improving network control.

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    Area of Science:

    • Control Theory
    • Network Synchronization
    • Dynamical Systems

    Background:

    • Discontinuous dynamic networks present challenges for achieving stable synchronization.
    • Existing fixed-time (FXT) synchronization methods require stricter conditions and offer less precise settling times.
    • Preassigned-time (PAT) synchronization needs robust control schemes independent of initial conditions and parameters.

    Purpose of the Study:

    • To develop improved stability conditions for fixed-time (FXT) synchronization.
    • To design simple and effective controllers for FXT and preassigned-time (PAT) synchronization in discontinuous networks.
    • To achieve synchronization within a prespecified time, independent of system initial states and parameters.

    Main Methods:

    • Establishing more relaxed conditions for FXT stability using special functions.
    • Developing a simple controller without linear feedback for FXT synchronization.
    • Designing novel control protocols with finite gains for PAT synchronization.

    Main Results:

    • Achieved more accurate settling time (ST) estimates for FXT synchronization.
    • Demonstrated successful FXT synchronization in discontinuous networks with a simplified controller.
    • Developed PAT synchronization protocols enabling prespecified, initial-value-independent synchronization times.
    • Validated improved stability and synchronization through two numerical examples.

    Conclusions:

    • The proposed methods offer enhanced FXT stability and accurate settling time estimations.
    • The developed controllers facilitate efficient FXT and PAT synchronization in complex discontinuous networks.
    • The findings contribute to more flexible and predictable network synchronization strategies.