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Novel Unified Stability Criterion For Fractional-Order Time Delay Systems With Strong Resistance To Fractional Orders

Author

Listed:
  • ZHE ZHANG

    (College of Electrical and Information Engineering, Hunan University, Hunan, 410082, P. R. China)

  • CHENGHAO XU

    (College of Electrical and Information Engineering, Hunan University, Hunan, 410082, P. R. China)

  • YAONAN WANG

    (College of Electrical and Information Engineering, Hunan University, Hunan, 410082, P. R. China)

  • JIANQIAO LUO

    (College of Electrical and Information Engineering, Hunan University, Hunan, 410082, P. R. China)

  • XU XIAO

    (College of Electrical and Information Engineering, Hunan University, Hunan, 410082, P. R. China)

Abstract

In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic stability, is only slightly affected by the change of the fractional order. In addition, the unified stability criterion is applied to general multi-dimensional nonlinear fractional-order systems with time delays, the corresponding asymptotic stability criterion is applied by combining the vector Lyapunov function with the M-matrix method. Compared with the traditional stability criterion, the unified stability criterion is slightly influenced by the changing fractional order and large time delays. The reliability and effectiveness of the novel uniform stability criterion were verified through three representative examples.

Suggested Citation

  • Zhe Zhang & Chenghao Xu & Yaonan Wang & Jianqiao Luo & Xu Xiao, 2024. "Novel Unified Stability Criterion For Fractional-Order Time Delay Systems With Strong Resistance To Fractional Orders," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-19.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:03:n:s0218348x24500452
    DOI: 10.1142/S0218348X24500452
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