Stability results for a class of difference systems with delay. (English) Zbl 1187.39025
Summary: Considering the linear delay difference system \(x(n+1)=ax(n)+Bx(n-k)\), where \(a\in (0,1), B\) is a \(p\times p\) 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.
MSC:
| 39A30 | Stability theory for difference equations |
Keywords:
linear delay difference system; stability domain; nonlinear difference systems; discrete-time Hopfield neural networksReferences:
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