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:	Hindawi Limited 2014-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2014/481971

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spelling	doaj-3f9ccea1f6074237a721f035d1ff6eef2020-11-24T23:02:57ZengHindawi LimitedAbstract 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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yanlei Wu
spellingShingle	Yanlei Wu Stability of Stochastic Differential Delay Systems with Delayed Impulses Abstract and Applied Analysis
author_facet	Yanlei Wu
author_sort	Yanlei Wu
title	Stability of Stochastic Differential Delay Systems with Delayed Impulses
title_short	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_sort	stability of stochastic differential delay systems with delayed impulses
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2014-01-01
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.
url	http://dx.doi.org/10.1155/2014/481971
work_keys_str_mv	AT yanleiwu stabilityofstochasticdifferentialdelaysystemswithdelayedimpulses
_version_	1725634351334424576

Stability of Stochastic Differential Delay Systems with Delayed Impulses

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