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Nyquist-based stability analysis of non-commensurate fractional-order delay systems

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  • Zhang, Shuo
  • Liu, Lu
  • Xue, Dingyu

Abstract

As a generalization of the first and second order models, the elementary fractional-order models have been widely used in various engineering fields. However, most of the previous studies only focus on commensurate fractional-order models. In this paper, a general non-commensurate elementary fractional-order delay system is investigated. First, the stability of the studied fractional-order delay system is analyzed based on Nyquist theorem. Then, a series of sufficient stability conditions are presented for different combinations of parameters, including the fractional orders (α, β), time delay (τ), pseudo-damping factor (ζ), and natural frequency (ω0). Finally, three examples are given to show the effectiveness of the presented results.

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  • Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320300801
    DOI: 10.1016/j.amc.2020.125111
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    Cited by:

    1. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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