Journal of Inequalities and Applications
Volume 2005 (2005), Issue 2, Pages 119-125

A note on asymptotic stability of delay difference systems

Hideaki Matsunaga

Department of Mathematical Sciences, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan

Received 9 September 2003; Revised 22 December 2004

Copyright © 2005 Hideaki Matsunaga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the linear delay difference system xn+1xn=Axnk, where A is a 2×2 real constant matrix and k 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 detA, trA, and the delay k.