Delay-independent stability of homogeneous systems

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 as...

Full description

Saved in:
Bibliographic Details
Published inApplied mathematics letters Vol. 34; pp. 43 - 50
Main Authors Aleksandrov, A.Yu, Zhabko, A.P.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.08.2014
Subjects
Approximation
Asymptotic properties
Asymptotic stability
Delay
Dynamical systems
Homogeneous systems
Lyapunov function
Mathematical analysis
Nonlinear dynamics
Nonlinearity
Oscillatory systems
Stability
Time-delay
Oscillatory systems
Asymptotic stability
Homogeneous systems
Time-delay
Lyapunov function
Online AccessGet full text

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2014.03.016