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Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional

Author

Listed:
  • Shuoting Wang

    (School of Computer, Chengdu University, Chengdu 610106, China)

  • Kaibo Shi

    (School of Electronic Information and Electrical Engineering, Chengdu University, Chengdu 610106, China)

  • Jin Yang

    (School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, China)

Abstract

In this paper, the asymptotic stability problem of neural networks with time-varying delays is investigated. First, a new sufficient and necessary condition on a general polynomial inequality was developed. Then, a novel augmented Lyapunov–Krasovskii functional (LKF) was constructed, which efficiently introduces some new terms related to the previous information of neuron activation function. Furthermore, based on the suitable LKF and the stated negative condition of the general polynomial, two criteria with less conservatism were derived in the form of linear matrix inequalities. Finally, two numerical examples were carried out to confirm the superiority of the proposed criteria, and a larger allowable upper bound of delays was achieved.

Suggested Citation

  • Shuoting Wang & Kaibo Shi & Jin Yang, 2022. "Improved Stability Criteria for Delayed Neural Networks via a Relaxed Delay-Product-Type Lapunov–Krasovskii Functional," Mathematics, MDPI, vol. 10(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2768-:d:880138
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    References listed on IDEAS

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    1. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," 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. Bingrui Xu & Bing Li, 2022. "Event-Triggered State Estimation for Fractional-Order Neural Networks," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    4. M. J. Park & O. M. Kwon & E. J. Cha, 2015. "On Stability Analysis for Generalized Neural Networks with Time-Varying Delays," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, October.
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    Cited by:

    1. Xinsong Yang & Ruofeng Rao, 2023. "Well-Posedness, Dynamics, and Control of Nonlinear Differential System with Initial-Boundary Value," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

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