Stability Results for a Class of Difference Systems with Delay
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...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2009/938492 |
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doaj-ae4b74162ade4f06acb8298e5b6f9ca02020-11-24T21:58:25ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472009-01-01200910.1155/2009/938492Stability Results for a Class of Difference Systems with DelayEva KaslikConsidering 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. http://dx.doi.org/10.1155/2009/938492 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Eva Kaslik |
| spellingShingle |
Eva Kaslik Stability Results for a Class of Difference Systems with Delay Advances in Difference Equations |
| author_facet |
Eva Kaslik |
| author_sort |
Eva Kaslik |
| title |
Stability Results for a Class of Difference Systems with Delay |
| title_short |
Stability Results for a Class of Difference Systems with Delay |
| title_full |
Stability Results for a Class of Difference Systems with Delay |
| title_fullStr |
Stability Results for a Class of Difference Systems with Delay |
| title_full_unstemmed |
Stability Results for a Class of Difference Systems with Delay |
| title_sort |
stability results for a class of difference systems with delay |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2009-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2009/938492 |
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AT evakaslik stabilityresultsforaclassofdifferencesystemswithdelay |
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