Convex Lyapunov functions for stability analysis of fractional order systems

被引：86
作者：
Chen, Weisheng [1 ]
Dai, Hao [1 ]
Song, Yanfei [1 ]
Zhang, Zhengqiang [2 ]
机构：
[1] Xidian Univ, Sch Aerosp Sci & Technol, Xian 710071, Peoples R China
[2] Qufu Normal Univ, Sch Elect Engn & Automat, Rizhao 276826, Peoples R China
来源：
IET CONTROL THEORY AND APPLICATIONS | 2017年 / 11卷 / 07期
基金：
中国国家自然科学基金;
关键词：
Lyapunov methods; stability; convex Lyapunov functions; stability analysis; fractional order systems; Mittag-Leffler stable system; convex positive definite function; negative-definite fractional order derivative; DIFFERENTIAL-EQUATIONS; NONLINEAR-SYSTEMS; SLIDING MODE; STABILIZATION;
D O I：
10.1049/iet-cta.2016.0950
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag-Leffler stable if there is a convex and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation.
引用
收藏
页码：1070 / 1074
页数：5
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