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    This study addresses synchronization in discrete-time neural networks (NNs) with uncertain connections. A novel approach using distributed impulsive observers and controllers ensures reliable information exchange and network synchronization.

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    Area of Science:

    • Control Theory
    • Artificial Intelligence
    • Network Science

    Background:

    • Synchronization of discrete-time neural networks (NNs) is crucial for complex information processing.
    • Uncertainty in connection weights leads to challenges in achieving reliable synchronization.
    • Existing methods may face limitations in communication load and control efficiency.

    Purpose of the Study:

    • To investigate and achieve synchronization for discrete-time neural networks with uncertain information exchange.
    • To design distributed impulsive observers and controllers to manage network uncertainties.
    • To establish a robust framework for ensuring stable and efficient network synchronization.

    Main Methods:

    • Formulating network uncertainties into a norm-bounded uncertain Laplacian matrix.
    • Designing distributed impulsive observers to reduce communication load and monitor NN states.
    • Developing an impulsive controller and an impulsive augmented error system (IAES) using matrix Kronecker product.
    • Proving the stability of the IAES to establish a sufficient condition for synchronization.

    Main Results:

    • A sufficient condition for the synchronization of discrete-time neural networks with uncertain Laplacian matrices was established.
    • An iterative algorithm was developed to determine optimal impulsive signal intervals and controller/observer gains.
    • The effectiveness of the proposed method was demonstrated through a numerical example, confirming successful synchronization.

    Conclusions:

    • The proposed distributed impulsive observer and controller design effectively ensures synchronization in discrete-time neural networks with uncertain connections.
    • The developed iterative algorithm provides a practical method for tuning control parameters.
    • This research contributes a robust and efficient approach to synchronization problems in uncertain network systems.