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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (5): 642-650.doi: 10.3969/j.issn.1005-3085.2020.05.010

• • 上一篇    

一类分数阶非线性时滞系统的稳定性与镇定（英）

赵   冬1,2,   李婷婷3,   尹  昊3   

  1. 1- 合肥工业大学管理学院，合肥  230009
    2- 淮北职业技术学院基础部，淮北  235000
    3- 合肥工业大学自动化系，合肥  230009
  • 收稿日期:2017-09-26 接受日期:2020-06-02 出版日期:2020-10-15 发布日期:2020-12-15

Stability and Stabilization of a Class of Fractional-order Nonlinear Delayed Systems

ZHAO Dong1,2,  LI Ting-ting3,   YIN Hao3   

  1. 1- School of Management, Hefei University of Technology, Hefei 230009
    2- Department of Basic, Huaibei Vocational Technical College, Huaibei 235000
    3- Department of Automation, Hefei University of Technology, Hefei 230009
  • Received:2017-09-26 Accepted:2020-06-02 Online:2020-10-15 Published:2020-12-15
  • Supported by:
    The National Natural Science Foundation of China (11571016).

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摘要： 稳定性是控制系统分析与设计的基础．探索分数阶系统，特别是分数阶时滞非线性系统的稳定性条件是控制理论与工程领域中的难点问题．本文研究了一类分数阶非线性时滞系统的稳定性和镇定．通过将原系统转化成等价的分数阶积分系统，再借助不等式放缩技术，提出了一个有效且形式简单的确保该类系统稳定新的时滞无关稳定性准则．根据所得的稳定条件，提出了基于时滞线性反馈控制器的镇定控制方法．最后，数值实例验证了所得结果的有效性．此外，本文所使用的方法可以推广和应用于其他类型的分数阶系统的稳定性和镇定控制．

关键词: 分数阶系统, 稳定性, 镇定性, 非线性系统, 线性反馈控制器

Abstract: Stability is the foundation of analysis and design of the control systems. To explore the stability conditions of the fractional-order systems, especially fractional-order nonlinear delayed systems, is one of the most difficult issues in the field of the control theory and engineering. This paper is concerned with stability and stabilization of a class of fractional-order nonlinear delayed systems. By transforming the systems into an equivalent fractional integral ones and using inequality scaling technique, a new effective sufficient stability condition with simple form is established for such systems. Based on the proposed the results, some stabilization criteria are also derived by designing time-delay linear feedback controller. Finally, a numerical example illustrates the effectiveness of the results. In addition, the proposed methods are also extended and applied to other type fractional-order systems.

Key words: fractional-order systems, stability, stabilization, nonlinear systems, linear feedback controller

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