Open Access

A note on asymptotic stability of delay difference systems

Journal of Inequalities and Applications20052005:764965

DOI: 10.1155/JIA.2005.119

Received: 9 September 2003

Published: 1 June 2005

Abstract

For the linear delay difference system https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq1_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq2_HTML.gif is a https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq3_HTML.gif real constant matrix and https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq4_HTML.gif is a nonnegative integer, we present an explicit necessary and sufficient condition for the asymptotic stability of the zero solution of this system in terms of https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq6_HTML.gif , and the delay https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.119/MediaObjects/13660_2003_Article_1552_IEq7_HTML.gif .

Authors’ Affiliations

(1)
Department of Mathematical Sciences, Osaka Prefecture University

Copyright

© Matsunaga. 2005