Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching

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• 作者：Yonggui Kao^a ; ^{ygkao2008@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Quanxin Zhu ; ^b ; ^{05401@njnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{zqx22@126.com" class="auth_mail" title="E-mail the corresponding author} ; Wenhai Qi^c ; ^{qiwhtanedu@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Impulsive ; Stochastic functional differential equation ; Markovian switching ; Exponential stability ; Instability
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：15 November 2015
• 年：2015
• 卷：271
• 期：Complete
• 页码：795-804
• 全文大小：352 K

文摘

In this paper, based on the Lyapunov second method and Razumikin techniques, we establish some novel criteria on pth moment exponential stability, almost exponential stability and instability of impulsive stochastic functional differential equations (ISFDEs) with Markovian switching. The findings show that impulsive stochastic functional equations with Markovian switching can be exponentially stabilized by impulses. Finally, an example is presented to illustrate the effectiveness and efficiency of the obtained results.