Convergent systems vs. incremental stability

被引：74

作者：

Rueffer, Bjoern S. ^{[1
]}

van de Wouw, Nathan ^{[2
]}

Mueller, Markus ^{[3
]}

机构：

[1] Univ Paderborn, Signal & Syst Theory Grp, EIM E, D-33098 Paderborn, Germany

[2] Eindhoven Univ Technol, Dept Mech Engn, NL-5600 MB Eindhoven, Netherlands

[3] Univ Exeter, Environm & Sustainabil Inst, Penryn TR10 9EZ, Cornwall, England

来源：

SYSTEMS & CONTROL LETTERS | 2013年 / 62卷 / 03期

关键词：

Convergent systems; Incremental stability; Time-varying nonlinear systems; Converse Lyapunov result; LYAPUNOV APPROACH;

D O I：

10.1016/j.sysconle.2012.11.015

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：277 / 285

页数：9

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