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Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov–Krasovskii functional

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  • Gao, Zhen-Man
  • He, Yong
  • Wu, Min

Abstract

The stability issue of neural networks with time-varying delay is investigated in this paper. Firstly, a kind of new augmented single integral which involves s-dependent integral terms (∫stx(θ)dθ and ∫st−d(t)x(θ)dθ) is proposed. Then, to further reduce the conservatism of stability criteria, one less-conservative LKF augmented integral terms (∫t−d(t)tx(θ)dθ,∫t−ht−d(t)x(θ)dθ,∫t−d(t)t∫stx(θ)d(t)dθds and ∫t−ht−d(t)∫st−d(t)x(θ)d(t)dθds) is employed, which considering more interrelation system states is employed. Finally, two numerical examples are employed to illustrate the effectiveness of proposed methods and the results verify the feasibility.

Suggested Citation

  • Gao, Zhen-Man & He, Yong & Wu, Min, 2019. "Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov–Krasovskii functional," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 258-269.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:258-269
    DOI: 10.1016/j.amc.2018.12.026
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Zhang, Bao-Lin & Cheng, Luhua & Pan, Kejia & Zhang, Xian-Ming, 2020. "Reducing conservatism of stability criteria for linear systems with time-varying delay using an improved triple-integral inequality," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    3. Chen, Jun & Park, Ju H., 2020. "New versions of Bessel–Legendre inequality and their applications to systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 375(C).

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