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Further results on exponential stability of neural networks with time-varying delay

Author

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  • Ji, Meng-Di
  • He, Yong
  • Wu, Min
  • Zhang, Chuan-Ke

Abstract

This paper investigates the problem of the exponential stability for a class of neural networks with time-varying delay. A triple integral term and a term considering the delay information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF). The obtained criterion show advantages over the existing ones since not only a novel LKF is constructed but also several techniques such as Wirtinger-based inequality and convex combination technique are used to estimate the upper bound of the derivative of the LKF. Finally, a numerical example is provided to verify the effectiveness and benefit of the proposed criterion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:175-182
    DOI: 10.1016/j.amc.2015.01.004
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    Citations

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    Cited by:

    1. Sun, Yonghui & Li, Ning & Shen, Mouquan & Wei, Zhinong & Sun, Guoqiang, 2018. "Robust H∞ control of uncertain linear system with interval time-varying delays by using Wirtinger inequality," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 1-11.
    2. Long, Fei & Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Wang, Qing-Guo & Wu, Min, 2018. "Stability analysis of Lur’e systems with additive delay components via a relaxed matrix inequality," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 224-242.
    3. 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.
    4. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    5. 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).
    6. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
    7. 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).
    8. Shao, Hanyong & Li, Huanhuan & Zhu, Chuanjie, 2017. "New stability results for delayed neural networks," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 324-334.

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