一类随机时滞微分系统的p-阶矩稳定性

发布时间：2018-06-13 10:21

本文选题：时滞 + 随机微分系统　；参考：《四川师范大学》2017年硕士论文

【摘要】：随机时滞微分系统是一种重要的数学模型,稳定性是随机时滞微分系统的一个基本问题.时滞和随机干扰常常会导致系统的稳定性变化.建立随机时滞微分系统稳定性的判别条件非常重要.通过构造恰当的Lyapunov泛函(或函数)来研究系统的稳定性是通常的做法,但构造Lyapunov泛函有一定的难度.使用其他技巧来研究随机时滞微分系统的稳定性是一种选择.本文中,我们将采用不等式技巧来研究随机时滞微分系统的稳定性,以避免Lyapunov泛函构造的困难.首先,对系统建立了一个适当的常数变易公式,并利用Jesen不等式、Burkholder-Davids-Gundy不等式、Holder不等式等分析技巧,得到了系统的吸引性和p-阶矩稳定性的充分条件,并给出数值实例,验证本文结果的有效性.其次,给出了随机时滞微分系统K-稳定性概念,并通过非负矩阵性质、BDG不等式、Holder不等式、反证等分析技巧建立了系统的K-全局p阶矩渐近稳定和K-全局p阶矩指数稳定.
[Abstract]:Stochastic delay differential system is an important mathematical model and stability is a basic problem of stochastic delay differential system. Time delay and random disturbance often lead to the stability change of the system. It is very important to establish the stability criteria for stochastic delay differential systems. It is common to study the stability of the system by constructing proper Lyapunov functional (or function), but it is difficult to construct Lyapunov functional. It is an option to use other techniques to study the stability of stochastic delay differential systems. In this paper, we will use inequality techniques to study the stability of stochastic delay differential systems so as to avoid the difficulty of constructing Lyapunov Functionals. First of all, an appropriate constant variation formula is established for the system. By using the analytical techniques such as the Jesen inequality and Burkholder-David Gundy inequality and Holder inequality, the sufficient conditions for the attractiveness of the system and the stability of the p-order moment are obtained, and a numerical example is given. The validity of the results is verified. Secondly, the concept of K-stability for stochastic delay differential systems is given, and the asymptotic stability of K-global p-order moments and the exponential stability of K-global p-order moments are established by using the nonnegative matrix properties of BDG inequality Holder inequality, inverse proof and other analytical techniques.
【学位授予单位】：四川师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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