Markov切换的脉冲随机泛函微分方程的指数稳定性

Exponential stability of ISFDEs with Markov switching

研究了一类具有Markov切换的脉冲随机泛函微分方程的全局p阶指数稳定性。通过利用Ito公式,引入一类特殊的Lyapunov函数,运用数学分析方法、Rzauminkin-型方法和不等式技巧建立了该系统全局p阶矩指数的稳定性定理,获得了其p阶矩Lyapunov指数的上限,改善和推广了相关文献的结果,并通过一个实例说明了本文结论具有更低的保守性。

A class of impulsive stochastic functional differential equations with Markov switching is investigated.Based on It formula and by introducing a class of special Lyapunov functions and applying mathematical analysis method,Lyapunov-Razumikhin method and combing with inequality technique,some novel sufficient conditions are derived to ensure the p th moment exponential stability of the trivial solution.A numerical example is given to illustrate the effectiveness and lower conservation.