求时滞系统最大实部本征值的一种数值算法  

An Algorithm for Calculating the Rightmost Characteristic Root(s) of Time-delay Systems

作　　者：王在华[1] 

机构地区：[1]解放军理工大学理学院,南京211101

出　　处：《应用泛函分析学报》2017年第1期16-22,共7页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金面上项目(11372354)

摘　　要：时滞动力系统是一类无穷维系统,其平衡点在Lyapunov意义下的渐近稳定性可由该系统的线性化系统的无穷多个本征值的分布来确定.在一定条件下,平衡点是渐近稳定的当且仅当最大实部本征值的实部小于零.本文给出了一种计算最大实部本征值的数值算法,只需要多次计算一个与本征函数及其导数的实函数的数值积分即可.该算法易于编程计算,并且增加时滞的个数并不增加稳定性分析的困难.利用本文算法计算了一阶中立型时滞微分方程的最大实部本征值.Time-delay system is a class of infinite dimensional systems, the asymp- totical stability in the sense of Lyapunov of an equilibrium of a time-delay system can be determined by the location of its infinite many of characteristic roots. Under certain conditions, the equilibrium is asymptotically stable if and only if the rightmost characteristic root（s） has negative real part. This paper presents an effective numerical algorithm for calculating the rightmost characteristic root（s）, by repeated estimations of a definite integral of a real function associated with the characteristic function and its derivative. The main advantages of the algorithm include： it is easy coded for implementation, and it does not increase much complexity when the number of time delays increases. The algorithm is applied for calculating the rightmost characteristic root（s） of a first-order neutral delay differential equation, for demonstration.

关 键 词：时滞 稳定性 本征值 

分 类 号：O175.9[理学—数学] O241.7[理学—基础数学]