Stability of Stochastic Differential Delay Systems with Delayed Impulses

We investigate the stability of stochastic delay differential systems with delayed impulses by Razumikhin methods. Some criteria on the pth moment and almost sure exponential stability are obtained. It is shown that an unstable stochastic delay system can be successfully stabilized by delayed impuls...

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Main Author: Yanlei Wu
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/481971
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author Yanlei Wu
author_facet Yanlei Wu
author_sort Yanlei Wu
collection DOAJ
description We investigate the stability of stochastic delay differential systems with delayed impulses by Razumikhin methods. Some criteria on the pth moment and almost sure exponential stability are obtained. It is shown that an unstable stochastic delay system can be successfully stabilized by delayed impulses. Moreover, it is also shown that if a continuous dynamic system is stable, then, under some conditions, the delayed impulses do not destroy the stability of the systems. The effectiveness of the proposed results is illustrated by two examples.
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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
publisher Wiley
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series Abstract and Applied Analysis
spelling doaj-art-3f9ccea1f6074237a721f035d1ff6eef2025-02-03T01:30:14ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/481971481971Stability of Stochastic Differential Delay Systems with Delayed ImpulsesYanlei Wu0Department of Mathematics, Anhui Polytechnic University, Wuhu, Anhui 241000, ChinaWe investigate the stability of stochastic delay differential systems with delayed impulses by Razumikhin methods. Some criteria on the pth moment and almost sure exponential stability are obtained. It is shown that an unstable stochastic delay system can be successfully stabilized by delayed impulses. Moreover, it is also shown that if a continuous dynamic system is stable, then, under some conditions, the delayed impulses do not destroy the stability of the systems. The effectiveness of the proposed results is illustrated by two examples.http://dx.doi.org/10.1155/2014/481971
spellingShingle Yanlei Wu
Stability of Stochastic Differential Delay Systems with Delayed Impulses
Abstract and Applied Analysis
title Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_full Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_fullStr Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_full_unstemmed Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_short Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_sort stability of stochastic differential delay systems with delayed impulses
url http://dx.doi.org/10.1155/2014/481971
work_keys_str_mv AT yanleiwu stabilityofstochasticdifferentialdelaysystemswithdelayedimpulses