Set-induced stability results for delay difference equations

R.H. Gielen, M. Lazar, S. Olaru

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

7 Citations (Scopus)

Abstract

This chapter focuses on the relation between stability of delay difference equations (DDEs) and the existence of D -contractive sets. Such sets are of importance as they provide a region of attraction, which is difficult to obtain for delay systems. Firstly, it is established that a DDE admits a D -contractive set if and only if it admits a Lyapunov-Razumikhin function. However, it is also shown that there exist stable DDEs that do not admit a D -contractive set. Therefore, secondly, further necessary conditions for the existence of a D -contractive set are established. These necessary conditions provide a first step towards the derivation of a notion of asymptotic stability for DDEs which is equivalent to the existence of a D -contractive set.
Original languageEnglish
Title of host publicationTime delay systems : methods, applications and new trends
EditorsR. Sipahi, T. Vyhlidal, S.-I. Niculescu, P. Pepe
PublisherSpringer
Pages73-84
DOIs
Publication statusPublished - 2012

Publication series

NameLecture Notes in Control and Information Sciences
Volume423
ISSN (Print)0170-8643

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