稳定性切换点法在时滞系统的鲁棒稳定性中的应用  

THE APPLICATION OF STABILITY SWITCHES POINT METHOD IN THE ROBUST STABILITY OF A CLASS OF TIME-DELAY SYSTEM

作　　者：狄成宽[1] 

机构地区：[1]南京工程学院应用数学研究所,南京211167

出　　处：《动力学与控制学报》2011年第2期111-116,共6页Journal of Dynamics and Control

摘　　要：讨论了一类参数与时滞相关的时滞系统的鲁棒稳定性.在"稳定性切换几何判据法"的基础上提出了"稳定性切换点法",使用该方法可得到相应方程零解稳定的参数变化区域.针对向日葵方程这一实际例子,利用文中所提出的方法并结合Maple软件作图可以容易地得到稳定性区域和不稳定性区域以及两区域的分界线、Hopf分岔点等;进一步通过对时滞大小的调控得到方程零解的鲁棒稳定性.The robust stability for a class of time-delay system with delay dependent parameters was discussed.On the basis of ＂geometric stability switches criteria＂,a new stabilization criterion ＂stability switches point method＂ was established.Using the new criterion,the region of the parameters which make the equilibrium asymptotically stable can be obtained easily.As an application,the sunflower equation was studied,and the result shows that one can obtain not only the stable region but also the Hopf bifurcation points with the help of mathematic software：Maple.Moreover,the robust stability of the equilibrium can be reached by adjusting the time delay to proper values.

关 键 词：时滞 稳定性切换 切换点 稳定性区域 鲁棒稳定性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]