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Novel stability results of multivariable fractional-order system with time delay

Author

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  • Zhang, Zhe
  • Wang, Yaonan
  • Zhang, Jing
  • Ai, Zhaoyang
  • Liu, Feng

Abstract

This paper deduces some novel asymptotic stability criteria for different forms of multivariable fractional-order systems (MFOS) whose fractional-order parameters are between 0 and 1 with time delays based on M-matrix. First, we extend the general asymptotic stability condition of ordinary systems to MFOS. Then, we investigate into the linear and nonlinear MFOS, then the asymptotic stability criterion of which derived based on M-matrix. Then, for the asymptotically stability study of the relatively complex MFOS with time delay, we also present the asymptotic stability criterion via the new method. In addition, we conduct an in-depth discussion on the stability of MFOS and integer order multivariable systems, and intuitively show the advantages of fractional-order systems through time responses. Compared with the fractional-order comparison principle, the new asymptotic stability criteria have the advantages of fewer restrictions, less conservativeness, and a wider applicability. Finally, four examples which contain MFOS covering different categories are shown.

Suggested Citation

  • Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001539
    DOI: 10.1016/j.chaos.2022.111943
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    References listed on IDEAS

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    Cited by:

    1. Zhang, Jia-Rui & Lu, Jun-Guo & Zhang, Qing-Hao, 2024. "Robust asymptotic stability analysis for fractional-order systems with commensurate time delays: The 1 < β ≤ 2 case," Applied Mathematics and Computation, Elsevier, vol. 475(C).

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