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

Shuo Zhang, Lu Liu and Dingyu Xue

Applied Mathematics and Computation, 2020, vol. 377, issue C

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.

Keywords: Fractional calculus; Stability analysis; Non-commensurate; Time delay; Nyquist theorem (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320300801

DOI: 10.1016/j.amc.2020.125111

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