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

被引：18
作者：
Zhang, Shuo [1 ]
Liu, Lu [2 ]
Xue, Dingyu [3 ]
机构：
[1] Northwestern Polytech Univ, Sch Math & Stat, Xian 710072, Peoples R China
[2] Northwestern Polytech Univ, Sch Marine Sci & Technol, Xian 710072, Peoples R China
[3] Northeastern Univ, Dept Informat Sci & Engn, Shenyang 110819, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2020年 / 377卷
基金：
中国国家自然科学基金; 中国博士后科学基金;
关键词：
Fractional calculus; Stability analysis; Non-commensurate; Time delay; Nyquist theorem; RESONANCE CONDITIONS; STABILIZATION; EQUATIONS;
D O I：
10.1016/j.amc.2020.125111
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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 (alpha, beta), time delay (tau), pseudo-damping factor (zeta), and natural frequency (omega(0)). Finally, three examples are given to show the effectiveness of the presented results. (C) 2020 Elsevier Inc. All rights reserved.
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页数：17
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