带有时滞脉冲的混杂随机微分系统的指数稳定性与脉冲镇定

发布时间：2018-05-16 07:58

本文选题：随机泛函微分系统 + 时滞脉冲　；参考：《安徽大学》2017年硕士论文

【摘要】：本学位论文主要对带有时滞脉冲的混杂随机微分系统的指数稳定性与脉冲镇定性展开研究,基于平均脉冲区间方法,Lyapunov函数,Razuminkhin型方法以及一些随机分析的技巧研究了带有时滞脉冲效应的混杂随机微分系统的指数稳定性及镇定问题.本文主要研究了以下内容:第一章,主要介绍了混杂脉冲随机微分系统的研究背景,意义以及前人做的科研成果.第二章,研究了带有时滞脉冲的混杂随机泛函微分系统的指数稳定性及脉冲镇定.利用平均脉冲区间,Lyapunov函数方法以及线性矩阵不等式(LMI)工具,建立了系统指数稳定及脉冲镇定的条件.特别是得到的结果摆脱了对脉冲序列最大或者最小脉冲区间的限制条件.因此,我们的结果有更少的保守性.最后,由两个例子有效地证明了结果的优越性.第三章,研究了带有时滞脉冲的混杂随机泛函微分系统的指数稳定性及时滞脉冲镇定.利用Lyapunov函数,Razuminkhin型方法以及一些随机分析的技巧得到了系统指数稳定以及时滞脉冲镇定的充分条件.特别是得到的结果表明脉冲的时滞部分也可以对系统稳定性起着好的作用.因此,所得到的结果可以适用更加广阔的范围.最后,三个例子有效地证明了结果的优越性.第四章,总结与展望.
[Abstract]:In this dissertation, the exponential stability and impulsive stabilization of hybrid stochastic differential systems with delays are studied. Based on the Lyapunov function Razuminkhin method and some techniques of stochastic analysis, the exponential stability and stabilization of hybrid stochastic differential systems with impulsive delay are studied. The main contents of this paper are as follows: in Chapter 1, the background, significance and achievements of hybrid impulsive stochastic differential systems are introduced. In chapter 2, we study the exponential stability and impulsive stabilization of hybrid stochastic functional differential systems with delay impulses. By using the mean impulse interval Lyapunov function method and the linear matrix inequality (LMI) tool, the conditions for exponential stability and impulsive stabilization of the system are established. In particular, the obtained results get rid of the limiting condition of the maximum or minimum pulse interval of the pulse sequence. As a result, our results are less conservative. Finally, the superiority of the result is proved by two examples. In chapter 3, the exponential stability and delay impulsive stabilization of hybrid stochastic functional differential systems with delay impulses are studied. By using the Lyapunov function Razuminkhin type method and some techniques of stochastic analysis, sufficient conditions for exponential stability and delay impulsive stabilization of the system are obtained. In particular, the results show that the delay part of impulses can also play a good role in the stability of the system. Therefore, the obtained results can be applied to a wider range. Finally, three examples prove the superiority of the result. Chapter four, summary and prospect.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63

【共引文献】