Almost Lyapunov functions for nonlinear systems

被引：12
|
作者：
Liu, Shenyu [1 ]
Liberzon, Daniel [1 ]
Zharnitsky, Vadim [2 ]
机构：
[1] Univ Illinois, Coordinated Sci Lab, Urbana, IL 61801 USA
[2] Univ Illinois, Dept Math, Urbana, IL USA
来源：
AUTOMATICA | 2020年 / 113卷
关键词：
Stability; Nonlinear systems; Lyapunov functions;
D O I：
10.1016/j.automatica.2019.108758
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 study convergence of nonlinear systems in the presence of an "almost Lyapunov" function which, unlike the classical Lyapunov function, is allowed to be nondecreasing - and even increasing - on a nontrivial subset of the phase space. Under the assumption that the vector field is free of singular points (away from the origin) and that the subset where the Lyapunov function does not decrease is sufficiently small, we prove that solutions approach a small neighborhood of the origin. A nontrivial example where this theorem applies is constructed. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：13
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