Advances in Difference Equations
Volume 2009 (2009), Article ID 938492, 13 pages
doi:10.1155/2009/938492
Research Article

Stability Results for a Class of Difference Systems with Delay

Eva Kaslik

Department of Mathematics and Computer Science, West University of Timisoara, Bd. C. Coposu 4, 300223 Timisoara, Romania

Received 2 November 2009; Accepted 13 December 2009

Academic Editor: Mariella Cecchi

Copyright © 2009 Eva Kaslik. 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.

Abstract

Considering the linear delay difference system x(n+1)=ax(n)+Bx(n-k), where a∈(0,1), B is a p×p real matrix, and k is a positive integer, the stability domain of the null solution is completely characterized in terms of the eigenvalues of the matrix B. It is also shown that the stability domain becomes smaller as the delay increases. These results may be successfully applied in the stability analysis of a large class of nonlinear difference systems, including discrete-time Hopfield neural networks.