本文選題：隨機(jī)泛函微分系統(tǒng) + 時(shí)滯脈沖�。� 參考：《安徽大學(xué)》2017年碩士論文

【摘要】：本學(xué)位論文主要對帶有時(shí)滯脈沖的混雜隨機(jī)微分系統(tǒng)的指數(shù)穩(wěn)定性與脈沖鎮(zhèn)定性展開研究,基于平均脈沖區(qū)間方法,Lyapunov函數(shù),Razuminkhin型方法以及一些隨機(jī)分析的技巧研究了帶有時(shí)滯脈沖效應(yīng)的混雜隨機(jī)微分系統(tǒng)的指數(shù)穩(wěn)定性及鎮(zhèn)定問題.本文主要研究了以下內(nèi)容:第一章,主要介紹了混雜脈沖隨機(jī)微分系統(tǒng)的研究背景,意義以及前人做的科研成果.第二章,研究了帶有時(shí)滯脈沖的混雜隨機(jī)泛函微分系統(tǒng)的指數(shù)穩(wěn)定性及脈沖鎮(zhèn)定.利用平均脈沖區(qū)間,Lyapunov函數(shù)方法以及線性矩陣不等式(LMI)工具,建立了系統(tǒng)指數(shù)穩(wěn)定及脈沖鎮(zhèn)定的條件.特別是得到的結(jié)果擺脫了對脈沖序列最大或者最小脈沖區(qū)間的限制條件.因此,我們的結(jié)果有更少的保守性.最后,由兩個(gè)例子有效地證明了結(jié)果的優(yōu)越性.第三章,研究了帶有時(shí)滯脈沖的混雜隨機(jī)泛函微分系統(tǒng)的指數(shù)穩(wěn)定性及時(shí)滯脈沖鎮(zhèn)定.利用Lyapunov函數(shù),Razuminkhin型方法以及一些隨機(jī)分析的技巧得到了系統(tǒng)指數(shù)穩(wěn)定以及時(shí)滯脈沖鎮(zhèn)定的充分條件.特別是得到的結(jié)果表明脈沖的時(shí)滯部分也可以對系統(tǒng)穩(wěn)定性起著好的作用.因此,所得到的結(jié)果可以適用更加廣闊的范圍.最后,三個(gè)例子有效地證明了結(jié)果的優(yōu)越性.第四章,總結(jié)與展望.
[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.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O211.63

【共引文獻(xiàn)】

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