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

Stability results for a class of difference systems with delay

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.