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Exponential stability of neural networks with a time-varying delay via a cubic function negative-determination lemma

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  • Chang, Xu-Kang
  • He, Yong
  • Gao, Zhen-Man

Abstract

The problem of global exponential stability of neural networks with a time-varying delay is studied in this article. Firstly, to fully utilize the cross-term relationships among state variables, an improved augmented delay-product-type Lyapunov-Krasovskii functional, including an extra double integral state, is established for the stability analysis. Accordingly, this augmented LKF derivative is a higher-order function of the time-varying delay. Then, three state vectors are considered to reduce the order of the function to cubic. So, to obtain the feasible negative-definiteness condition of this LKF derivative of non-convexity, a negative-determination lemma for cubic functions is employed to handle this problem. As a result, a novel stability criterion is obtained. Two well-known numerical examples illustrate the effectiveness of the criterion.

Suggested Citation

  • Chang, Xu-Kang & He, Yong & Gao, Zhen-Man, 2023. "Exponential stability of neural networks with a time-varying delay via a cubic function negative-determination lemma," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    • Handle: RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006750
    DOI: 10.1016/j.amc.2022.127602
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    References listed on IDEAS

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    1. Zeng, Hong-Bing & Zhai, Zheng-Liang & Wang, Wei, 2021. "Hierarchical stability conditions of systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    2. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    3. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    4. Ji, Meng-Di & He, Yong & Wu, Min & Zhang, Chuan-Ke, 2015. "Further results on exponential stability of neural networks with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 175-182.
    5. Wang, Chen-Rui & He, Yong & Lin, Wen-Juan, 2021. "Stability analysis of generalized neural networks with fast-varying delay via a relaxed negative-determination quadratic function method," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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    Cited by:

    1. Arunagirinathan, S. & Lee, T.H., 2024. "Generalized delay-dependent reciprocally convex inequality on stability for neural networks with time-varying delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 109-120.

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