Delay-independent stability of homogeneous systems

被引：28

作者：

Aleksandrov, A. Yu. ^{[1
]}

Zhabko, A. P. ^{[1
]}

机构：

[1] St Petersburg State Univ, Fac Appl Math & Control Proc, St Petersburg 198504, Russia

来源：

APPLIED MATHEMATICS LETTERS | 2014年 / 34卷

关键词：

Homogeneous systems; Time-delay; Asymptotic stability; Lyapunov function; Oscillatory systems; COOPERATIVE SYSTEMS; TIME-DELAY;

D O I：

10.1016/j.aml.2014.03.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A class of nonlinear systems with homogeneous right-hand sides and time-varying delay is studied. It is assumed that the trivial solution of a system is asymptotically stable when delay is equal to zero. By the usage of the Lyapunov direct method and the Razumikhin approach, it is proved that the asymptotic stability of the zero solution of the system is preserved for an arbitrary continuous nonnegative and bounded delay. The conditions of stability of time-delay systems by homogeneous approximation are obtained. Furthermore, it is shown that the presented approaches permit to derive delay-independent stability conditions for some types of nonlinear systems with distributed delay. Two examples of nonlinear oscillatory systems are given to demonstrate the effectiveness of our results. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：43 / 50

页数：8

共 23 条

[11] Stability theory for nonnegative and compartmental dynamical systems with time delay [J].

Haddad, WM ;

Chellaboina, VS .

SYSTEMS & CONTROL LETTERS, 2004, 51 (05) :355-361

[12]

Hale J.K., 1993, INTRODUCTION TO FUNC

[13]

Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics

[14] Lyapunov stability analysis for nonlinear delay systems [J].

Mazenc, F. ;

Niculescu, S.-I. .

Systems and Control Letters, 2001, 42 (04) :245-251

[15]

Ngoc P.H.A., 2012, APPL MATH LETT, V25, P1208

[16]

Niculescu S., 2001, LECTURE NOTES IN CON

[17] Novel stability criterion of time delay systems with nonlinear uncertainties [J].

Park, JH ;

Kwon, O .

APPLIED MATHEMATICS LETTERS, 2005, 18 (06) :683-688

[18]

Park Ju.H., 2009, APPL MATH LETT, V22, P1412

[19]

Post, 2000, STABILITY ISSUES AMB

[20]

Rasvan V., 2004, UNSOLVED PROBLEMS MA, P212

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