Open Access

Stability Results for a Class of Difference Systems with Delay

Advances in Difference Equations20102009:938492

https://doi.org/10.1155/2009/938492

Received: 2 November 2009

Accepted: 13 December 2009

Published: 7 February 2010

Abstract

Considering the linear delay difference system , where , is a real matrix, and is a positive integer, the stability domain of the null solution is completely characterized in terms of the eigenvalues of the matrix . 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.

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Authors’ Affiliations

(1)
Department of Mathematics and Computer Science, West University of Timisoara

Copyright

© Eva Kaslik. 2009

This article is published under license to BioMed Central Ltd. 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.