Finite-time stability of continuous autonomous systems

被引：4384

作者：

Bhat, SP ^{[1
]}

Bernstein, DS

机构：

[1] Indian Inst Technol, Dept Aerosp Engn, Powai 400076, Mumbai, India

[2] Univ Michigan, Dept Aerosp Engn, Ann Arbor, MI 48109 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2000年 / 38卷 / 03期

关键词：

stability; finite-time stability; non-Lipschitzian dynamics;

D O I：

10.1137/S0363012997321358

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Finite-time stability is defined for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Holder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov results involving scalar differential inequalities are given for finite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov functions. Finally, the sensitivity of finite-time-stable systems to perturbations is investigated.

引用

页码：751 / 766

页数：16

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