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Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays

Author

Listed:
  • Zhixin Zhang

    (School of Mathematics Sciences, Anhui University, Hefei 230601, China)

  • Yufeng Zhang

    (School of Mathematics Sciences, Anhui University, Hefei 230601, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
    School of Mathematics, Southeast University, Nanjing 210096, China)

  • Jiang Wei

    (School of Mathematics Sciences, Anhui University, Hefei 230601, China)

Abstract

In this paper, the global asymptotical stability of Riemann-Liouville fractional-order neural networks with time-varying delays is studied. By combining the Lyapunov functional function and LMI approach, some sufficient criteria that guarantee the global asymptotical stability of such fractional-order neural networks with both discrete time-varying delay and distributed time-varying delay are derived. The stability criteria is suitable for application and easy to be verified by software. Lastly, some numerical examples are presented to check the validity of the obtained results.

Suggested Citation

  • Zhixin Zhang & Yufeng Zhang & Jia-Bao Liu & Jiang Wei, 2019. "Global Asymptotical Stability Analysis for Fractional Neural Networks with Time-Varying Delays," Mathematics, MDPI, vol. 7(2), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:138-:d:202771
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    References listed on IDEAS

    as
    1. 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.
    2. Čermák, Jan & Došlá, Zuzana & Kisela, Tomáš, 2017. "Fractional differential equations with a constant delay: Stability and asymptotics of solutions," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 336-350.
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