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    This study addresses discrete Markov jump neural network synchronization using an event-triggered communication model. Novel methods ensure reliable synchronization despite communication constraints and asynchronous phenomena.

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    Area of Science:

    • Control Systems Engineering
    • Networked Systems
    • Computational Neuroscience

    Background:

    • Synchronization is crucial for networked systems like Markov jump neural networks (MJNNs).
    • Existing methods often overlook practical communication constraints such as event-triggered transmission, quantization, and asynchronous phenomena.
    • Conserving communication resources while maintaining system performance is a significant challenge.

    Purpose of the Study:

    • To investigate the synchronization issue of discrete Markov jump neural networks (MJNNs).
    • To propose a universal communication model incorporating event-triggered transmission, logarithmic quantization, and asynchronous phenomena.
    • To develop asynchronous output feedback controllers for MJNNs with potentially unavailable state information.

    Main Methods:

    • A universal communication model with event-triggered transmission, logarithmic quantization, and asynchronous phenomena.
    • A generalized event-triggered protocol using a diagonal matrix threshold parameter.
    • Hidden Markov Model (HMM) for mode mismatch, and a novel decoupling strategy for asynchronous output feedback controllers.
    • Lyapunov techniques and linear matrix inequalities (LMIs) to derive synchronization conditions.

    Main Results:

    • Sufficient conditions for dissipative synchronization of MJNNs were established using LMIs and Lyapunov methods.
    • A more general event-triggered protocol was developed, reducing conservatism.
    • A hidden Markov model (HMM) approach effectively handled mode mismatch due to time lags and packet dropouts.
    • Asynchronous output feedback controllers were designed, even when node state information is unavailable.

    Conclusions:

    • The proposed methods ensure effective and dissipative synchronization for discrete Markov jump neural networks under practical communication constraints.
    • The developed communication model and control strategies offer reduced conservatism and computational cost.
    • Numerical examples validated the effectiveness of the proposed synchronization approach.