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Advances in Continuous and Discrete Models

Theory and Modern Applications

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Stability Results for a Class of Difference Systems with Delay

Advances in Difference Equations volume 2009, Article number: 938492 (2010) Cite this article

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

    Eva Kaslik

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  1. Eva Kaslik
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Correspondence to Eva Kaslik.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cite this article

Kaslik, E. Stability Results for a Class of Difference Systems with Delay. Adv Differ Equ 2009, 938492 (2010). https://doi.org/10.1155/2009/938492

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

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation