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Stability Results for a Class of Difference Systems with Delay

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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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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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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Keywords

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