Lyapunov functions for nabla discrete fractional order systems

被引：56
|
作者：
Wei, Yiheng [1 ]
Chen, Yuquan [1 ]
Liu, Tianyu [1 ]
Wang, Yong [1 ]
机构：
[1] Univ Sci & Technol China, Dept Automat, Hefei 230026, Anhui, Peoples R China
来源：
ISA TRANSACTIONS | 2019年 / 88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：
Discrete fractional calculus; Lyapunov function; Asymptotic stability; Young inequality; STABILITY ANALYSIS;
D O I：
10.1016/j.isatra.2018.12.016
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 paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for each definition. With the help of the developed inequalities, the sufficient conditions can be obtained to guarantee the asymptotic stability of the nabla discrete fractional order nonlinear systems. Finally, three illustrative examples are presented to demonstrate the validity and feasibility of the proposed theoretical results. (C) 2018 ISA. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码：82 / 90
页数：9
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