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Updated: Mar 14, 2026

Using Neuron Spiking Activity to Trigger Closed-Loop Stimuli in Neurophysiological Experiments
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Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks.

Yin Sheng, Yi Shen, Mingfu Zhu

    IEEE Transactions on Neural Networks and Learning Systems
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    Summary
    This summary is machine-generated.

    This study presents new criteria for the global exponential stability of delayed recurrent neural networks (DRNNs). These findings enhance stability analysis for DRNNs using advanced mathematical techniques.

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    Area of Science:

    • Control Engineering
    • Computational Neuroscience
    • Applied Mathematics

    Background:

    • Delayed recurrent neural networks (DRNNs) are crucial in modeling complex dynamical systems.
    • Ensuring the stability of DRNNs is essential for reliable system performance and prediction.
    • Existing methods often lack delay-dependent criteria or precise convergence rate estimation.

    Purpose of the Study:

    • To derive novel delay-dependent criteria for global exponential stability of DRNNs.
    • To develop a general lemma for analyzing the exponential stability of DRNNs.
    • To extend existing global asymptotic stability results to global exponential stability.

    Main Methods:

    • Construction of an augmented Lyapunov-Krasovskii functional.
    • Application of the reciprocally convex combination approach.
    • Utilization of Wirtinger-based integral inequalities to derive linear matrix inequality conditions.

    Main Results:

    • New delay-dependent global exponential stability criteria for DRNNs are established.
    • A general lemma is proposed for estimating the exponential convergence rate.
    • The proposed lemma allows for the generalization of existing stability results.

    Conclusions:

    • The derived criteria and methods provide effective tools for analyzing DRNN stability.
    • The results offer improved insights into the dynamic behavior of delayed neural networks.
    • Numerical examples validate the proposed theoretical advancements.