@inbook{b871d45dd28f49f4a092ef138465505e,
title = "Set-induced stability results for delay difference equations",
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.",
author = "R.H. Gielen and M. Lazar and S. Olaru",
year = "2012",
doi = "10.1007/978-3-642-25221-1\_6",
language = "English",
series = "Lecture Notes in Control and Information Sciences",
publisher = "Springer",
pages = "73--84",
editor = "R. Sipahi and T. Vyhlidal and S.-I. Niculescu and P. Pepe",
booktitle = "Time delay systems : methods, applications and new trends",
address = "Germany",
}