| Автор | Braverman, Elena |
| Автор | Karabash, Illya M. |
| Дата выпуска | 2012 |
| dc.description | The relation between the following two properties of linear difference equations with infinite delay is investigated: (i) exponential stability and (ii) -input -state stability (Perron's property) which means that solutions of the non-homogeneous equation with zero initial data belong to when non-homogeneous terms are in . It is assumed that at each moment the prehistory (the sequence of preceding states) belongs to some weighted -space with an exponentially fading weight (the phase space). Our main result states that whenever and a certain boundedness condition on coefficients is fulfilled. This condition is sharp and ensures that, to some extent, exponential and -input -state stabilities do not depend on the choice of a phase space and parameters p and q. -input -state stability corresponds to uniform stability. We provide some evidence that similar criteria should not be expected for non-fading memory spaces. |
| Формат | application.pdf |
| Издатель | Taylor & Francis Group |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Тема | difference equations |
| Тема | unbounded delay |
| Тема | exponential stability |
| Тема | uniform stability |
| Тема | Perron's property |
| Тема | phase space |
| Тема | 39A11 |
| Тема | 39A10 |
| Тема | 39A06 |
| Тема | 39A12 |
| Название | Bohl–Perron-type stability theorems for linear difference equations with infinite delay |
| Тип | research-article |
| DOI | 10.1080/10236198.2010.531276 |
| Electronic ISSN | 1563-5120 |
| Print ISSN | 1023-6198 |
| Журнал | Journal of Difference Equations and Applications |
| Том | 18 |
| Первая страница | 909 |
| Последняя страница | 939 |
| Аффилиация | Braverman, Elena; Department of Mathematics and Statistics, University of Calgary |
| Аффилиация | Karabash, Illya M.; Department of Mathematics and Statistics, University of Calgary; Institute of Applied Mathematics and Mechanics |
| Выпуск | 5 |
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