Exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses via Razumikhin method

Advances in Difference Equations

Lijun Pan¹  Jinde Cao² 

[1] Department of Mathematics, Southeast University, Nanjing, P. R. China;School of Mathematics, Jia Ying University, Meizhou Guangdong, P. R. China

关键词: Razumikhin theorem;    stochastic functional differential equations;    impulse;    M-matrix;    Markovian chain;   

DOI  :  10.1186/1687-1847-2012-61

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, by using Razumikhin-type technique, we investigate p th moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several stability theorems of impulsive hybrid stochastic functional differential equations are derived. It is assumed that the state variables on the impulses can relate to the finite delay. These new results are employed to a class of n-dimensional linear impulsive hybrid stochastic systems with bounded time-varying delay. Moreover, an effective M-matrix method is introduced to study the exponential stability of these hybrid systems. Meanwhile, some examples and simulations are given to show our results.

【 授权许可】

CC BY