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Asymptotic stability versus exponential stability in linear volterra difference equations of convolution type |
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| Authors: | Saber Elaydi Satoru Murakami |
| Affiliation: | 1. Department of Mathematics , Trinity university , San Antonio , Texas , 78212 , USA;2. Department of Applied Mathematics , Okayama University of Science , Okayama , 1-1 Ridai-cho , 700 , Japan |
| Abstract: | It is shown that uniform asymptotic stability does not imply exponential stability in linear Volterra difference equations. However, if the kernel of the equation decays exponentially. then both concepts are equivalent as in the case of ordinary difference equations. |
| Keywords: | asymptotic stability exponential stability Volterra equations Z-transform difference equations resolvent |