Stability analysis of fractional differential time-delay equations

被引：21
|
作者：
Thanh, Nguyen T. [1 ]
Hieu Trinh [2 ]
Phat, Vu N. [3 ]
机构：
[1] Univ Min & Geol, Dept Math, Hanoi, Vietnam
[2] Deakin Univ, Sch Engn, Geelong, Vic 3217, Australia
[3] VAST, Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam
来源：
IET CONTROL THEORY AND APPLICATIONS | 2017年 / 11卷 / 07期
关键词：
Lyapunov methods; delays; Laplace transforms; asymptotic stability; stability analysis; fractional differential time-delay equations; Lyapunov function method; Caputo fractional derivatives; Laplace transform; Mittag-Leffler function; exponential boundedness; finite-time stability; ORDER SYSTEMS;
D O I：
10.1049/iet-cta.2016.1107
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 provides a novel analytical approach to studying the solutions and stability of fractional differential delay equations without using Lyapunov function method. By applying the properties of Caputo fractional derivatives, the Laplace transform and the Mittag-Leffler function, the authors first provide an explicit formula and solution bounds for the solutions of linear fractional differential delay equations. Then, they prove new sufficient conditions for exponential boundedness, asymptotic stability and finite-time stability of such equations. The results are illustrated by numerical examples.
引用
收藏
页码：1006 / 1015
页数：10
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