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    Area of Science:

    • Control Theory
    • Neural Networks
    • Systems Engineering

    Background:

    • Master-slave synchronization is crucial for complex systems.
    • Delayed neural networks present unique control challenges.
    • Time-varying control offers flexibility but complicates stability analysis.

    Purpose of the Study:

    • To investigate the master-slave synchronization of delayed neural networks.
    • To develop a general framework for time-varying control strategies.
    • To address stability issues under control failure scenarios.

    Main Methods:

    • Recasting synchronization as a stability problem for a delayed system.
    • Utilizing the Lyapunov-Razumikhin theorem.
    • Establishing a main theorem based on the time average of control gain.

    Main Results:

    • A novel theorem for master-slave synchronization of delayed neural networks.
    • The framework accommodates various intermittent control schemes.
    • A method to regain stability following control failure is proposed.

    Conclusions:

    • The developed theorem provides a robust solution for synchronization problems.
    • The findings are applicable to systems with intermittent or failing control.
    • Numerical examples validate the effectiveness of the proposed methods.