Journal of Inequalities and Applications 
Volume 2005 (2005), Issue 2, Pages 119-125
doi:10.1155/JIA.2005.119

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

Abstract

For the linear delay difference system xn+1−xn=Axn−k, 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.