Strict Lyapunov Functions for Homogeneous Time-Varying Systems

被引：2

作者：

Zhang, Bin ^{[1
]}

Jia, Yingmin ^{[2
]}

Du, Junping ^{[3
]}

机构：

[1] Beijing Univ Posts & Telecommun, Sch Automat, Beijing 100876, Peoples R China

[2] Beihang Univ, Res Div 7, Beijing 100191, Peoples R China

[3] Beijing Univ Posts & Telecommun, Sch Comp Sci, Beijing 100876, Peoples R China

来源：

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS | 2021年 / 51卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Lyapunov methods; Time-varying systems; Asymptotic stability; Tools; Stability criteria; TV; Homogeneous auxiliary systems; strict Lyapunov functions (SLFs); time-varying systems (TVSs);

D O I：

10.1109/TSMC.2019.2912208

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We provide new criterion and a class of strict Lyapunov functions (SLFs) for time-varying systems (TVSs) with zero homogeneity. The definition of homogeneous auxiliary system is given, where it is assumed that certain homogeneous functions are admitted with their derivatives, in terms of the error systems, bounded by periodic functions. Based on the homogeneous auxiliary system, sufficient conditions of uniform asymptotical stability for TVSs are formulated using the homogeneity framework. Unlike existing results, where non-SLFs or persistence of excitation condition are required, our criterion is greatly relaxed for broad classes of systems. The utility of our result is illustrated by case-study of pendulum stability with quasi-periodical frictions.

引用

页码：1994 / 2002

页数：9

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