On global asymptotic stability of <(x) over dot> = -φ(t)φT(t)x with φ not persistently exciting

被引：38

作者：

Barabanov, Nikita ^{[1
,2
]}

Ortega, Romeo ^{[3
]}

机构：

[1] North Dakota State Univ, Dept Math, Fargo, ND 58105 USA

[2] ITMO Univ, Dept Control Syst & Informat, St Petersburg 197101, Russia

[3] CNRS SUPELEC, Lab Signaux & Syst, F-91192 Gif Sur Yvette, France

来源：

SYSTEMS & CONTROL LETTERS | 2017年 / 109卷

关键词：

Linear time-varying systems; Stability theory; Persistency of excitation;

D O I：

10.1016/j.sysconle.2017.09.005

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 global convergence to zero of the solutions of the nth order differential equation <(x) over dot> = phi(t)phi(T)(t)x. We are interested in the case when the vector phi is not persistently exciting, which is a necessary and sufficient condition for global exponential stability. In particular, we establish new necessary conditions on phi(t) for global asymptotic stability of the zero equilibrium of the "unexcited" system. A new sufficient condition, that is strictly weaker than the ones reported in the literature, is also established. Unfortunately, it is also shown that this condition is not necessary. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：24 / 29

页数：6

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