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Global Exponential Stability Conditions for Discrete-Time BAM Neural Networks Affected by Impulses and Time-Varying Delays

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Abstract

This paper studies global exponential stability (GES) of discrete-time (D-T) BAM neural networks (BAMNNs) affected by impulses and time-varying delays. An impulse-free D-T BAMNN with time-varying delays is first developed via the properties of M-matrices, and then the relation between the solutions of the original and new BAMNNs is established. From which, sufficient conditions for GES of the original BAMNN are derived by investigating GES conditions of the new BAMNN based on the counter-evidence and the nature of the nonsingular M-matrix. The results of illustrative examples show that the obtained GES criteria are effective. By comparing with previous results, this paper has the following three merits: (a) the obtained GES criteria are to check the positivity of eigenvalues of a constant matrix, which is easy to realize; (b) this method can be used for other D-T system models affected by impulses and time-varying delays; and (c) the numerical results show that our method is less conservative than ones in other literatures.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

This work was supported by the Natural Science Foundation of Heilongjiang Province, China (YQ2021F014), the Basic Research Foundation for Outstanding Young Teachers in Heilongjiang Provincial Universities of China (Grant No. YQJH2023141), and the Fundamental Research Funds in Heilongjiang Provincial Universities of China (2022-KYYWF-1099). The authors would like to thank the anonymous associate editor and reviewers for their helpful comments and suggestions, which greatly improves the original version of the paper.

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Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Wanning Li, Xian Zhang & Xiaona Yang

  2. Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, 150080, China

    Wanning Li, Xian Zhang & Xiaona Yang

  3. School of Information Management, Heilongjiang University, Harbin, 150080, China

    Chunyan Liu

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  1. Wanning Li
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Li, W., Zhang, X., Liu, C. et al. Global Exponential Stability Conditions for Discrete-Time BAM Neural Networks Affected by Impulses and Time-Varying Delays. Circuits Syst Signal Process (2024). https://doi.org/10.1007/s00034-024-02701-6

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