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LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays

Author

Listed:
  • Hai Zhang
  • Renyu Ye
  • Song Liu
  • Jinde Cao
  • Ahmad Alsaedi
  • Xiaodi Li

Abstract

This paper is concerned with the asymptotic stability of the Riemann–Liouville fractional-order neural networks with discrete and distributed delays. By constructing a suitable Lyapunov functional, two sufficient conditions are derived to ensure that the addressed neural network is asymptotically stable. The presented stability criteria are described in terms of the linear matrix inequalities. The advantage of the proposed method is that one may avoid calculating the fractional-order derivative of the Lyapunov functional. Finally, a numerical example is given to show the validity and feasibility of the theoretical results.

Suggested Citation

  • Hai Zhang & Renyu Ye & Song Liu & Jinde Cao & Ahmad Alsaedi & Xiaodi Li, 2018. "LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 537-545, February.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:3:p:537-545
    DOI: 10.1080/00207721.2017.1412534
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    Cited by:

    1. Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Zhang, Hai & Cheng, Jingshun & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2021. "Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    4. Karthick, S.A. & Sakthivel, R. & Ma, Y.K. & Mohanapriya, S. & Leelamani, A., 2019. "Disturbance rejection of fractional-order T-S fuzzy neural networks based on quantized dynamic output feedback controller," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 846-857.
    5. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    6. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    7. Zhanying Yang & Jie Zhang, 2019. "Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays," Complexity, Hindawi, vol. 2019, pages 1-22, October.
    8. Stamov, Gani & Stamova, Ivanka & Martynyuk, Anatoliy & Stamov, Trayan, 2021. "Almost periodic dynamics in a new class of impulsive reaction–diffusion neural networks with fractional-like derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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