New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay  

区间变时滞Lurie系统的绝对稳定新准则(英文)

作　　者：薛明香[1,2] 费树岷[1] 李涛[3] 潘俊涛[1] 

机构地区：[1]东南大学复杂工程系统测量与控制教育部重点实验室,南京210096 [2]安徽大学数学科学学院,合肥230601 [3]南京航空航天大学自动化学院,南京210007

出　　处：《Journal of Southeast University(English Edition)》2011年第4期375-378,共4页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.60835001,60875035,60905009,61004032,61004064,11071001);China Postdoctoral Science Foundation(No.201003546);the Ph.D.Programs Foundation of Ministry of Education of China(No.20093401110001);the Major Program of Higher Education of Anhui Province(No.KJ2010ZD02);the Natural Science Research Project of Higher Education of Anhui Province(No.KJ2011A020)

摘　　要：The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.研究了一类具有区间变时滞的Lurie系统时滞相关绝对稳定性问题.利用增广Lyapunov泛函,结合自由权矩阵方法和反凸组合技术,提出了一种新的基于线性矩阵不等式的稳定性条件.通过保留Lyapunov泛函导数中常被忽略的有用信息,使得到的稳定性充分条件不仅依赖于时滞的上下界和时滞导函数的上下界,还依赖于它们的差,与已有文献的结果相比,具有更广泛的应用背景.此外,在处理非线性函数的扇形域时,给出了非线性函数的一种新的等式描述,和已有文献中的凸描述相比,要验证的线性矩阵不等式较少,因此具有更低的保守性.仿真实例表明了所提方法的有效性.

关 键 词：Lurie system reciprocal convex technique absolute stability interval time-varying delay linear matrix inequality （LMI） 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]