發(fā)布時(shí)間：2018-11-18 12:48

【摘要】：在電子工程、醫(yī)學(xué)和生物領(lǐng)域中,時(shí)滯問題普遍存在。為了更精確地刻畫事物的運(yùn)動(dòng)規(guī)律,含有時(shí)滯的泛函微分方程得到了越來越多的研究。本文主要分析了一類積分時(shí)滯系統(tǒng)的穩(wěn)定性及魯棒穩(wěn)定性,包括穩(wěn)定性定理,指數(shù)穩(wěn)定的充分條件以及數(shù)值求解方法,并探討了其在中立型隨機(jī)微分系統(tǒng)穩(wěn)定性問題中的應(yīng)用。首先,文章基于一般積分時(shí)滯系統(tǒng)的Lyapunov型穩(wěn)定性定理,通過選擇合適的Lyapunov函數(shù),并運(yùn)用不等式放縮技巧,建立了一類保證積分時(shí)滯系統(tǒng)穩(wěn)定的基于線性矩陣不等式的充分條件。其次,分析了此類系統(tǒng)的魯棒穩(wěn)定性問題,通過對(duì)原有系統(tǒng)的不同項(xiàng)上施加擾動(dòng),討論系統(tǒng)的魯棒穩(wěn)定性,同樣構(gòu)造了保證系統(tǒng)穩(wěn)定的一類Lyapunov泛函的形式,進(jìn)而給出了當(dāng)有擾動(dòng)作用時(shí),系統(tǒng)的魯棒穩(wěn)定性定理,并給出了相應(yīng)的證明。進(jìn)而,本文給出了數(shù)值例子來驗(yàn)證所給出結(jié)論的實(shí)際應(yīng)用性,針對(duì)充分條件,舉出數(shù)值例子,求出系統(tǒng)穩(wěn)定對(duì)應(yīng)的時(shí)滯范圍,從而驗(yàn)證本文已得出的結(jié)論的有效性。并與一些之前已有的結(jié)論做出對(duì)比來驗(yàn)證保守性。最后,作為積分時(shí)滯系統(tǒng)的一個(gè)應(yīng)用,文章討論了一類含有分布時(shí)滯和布朗運(yùn)動(dòng)的中立型隨機(jī)微分方程的穩(wěn)定性問題,此類系統(tǒng)的穩(wěn)定性與前面討論的積分時(shí)滯系統(tǒng)密切相關(guān)。利用積分時(shí)滯系統(tǒng)穩(wěn)定的相關(guān)條件,建立了判斷此類隨機(jī)微分方程均方穩(wěn)定的一組充分條件。
[Abstract]:In the fields of electronic engineering, medicine and biology, the problem of time delay is common. In order to describe the law of motion more and more accurately, functional differential equations with time delay have been studied more and more. In this paper, the stability and robust stability of a class of integro-delay systems are analyzed, including stability theorems, sufficient conditions for exponential stability and numerical solutions, and their applications to the stability problems of neutral stochastic differential systems are discussed. Firstly, based on the Lyapunov type stability theorem of general integral delay systems, by selecting appropriate Lyapunov functions and using the technique of inequality scaling, the sufficient conditions based on linear matrix inequalities (LMI) for the stability of integral delay systems are established. Secondly, the problem of robust stability of this kind of systems is analyzed. The robust stability of the system is discussed by perturbation on different terms of the original system, and a class of Lyapunov functional forms which guarantee the stability of the system are also constructed. Furthermore, the robust stability theorem for the system with perturbation is given, and the corresponding proof is given. Furthermore, a numerical example is given to verify the practical application of the proposed conclusion. For sufficient conditions, numerical examples are given to obtain the time-delay range corresponding to the stability of the system, thus validating the validity of the conclusions obtained in this paper. And compared with some previous conclusions to verify the conservatism. Finally, as an application of integral delay systems, this paper discusses the stability of a class of neutral stochastic differential equations with distributed delays and Brownian motions. The stability of such systems is closely related to the integral delay systems discussed previously. A set of sufficient conditions for judging the mean square stability of such stochastic differential equations are established by using the relative conditions for the stability of integro-delay systems.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O211.63
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本文編號(hào)：2340077