一类积分时滞切换系统的指数稳定  

Exponential stability of a class of switched systems with integral delay

作　　者：刘玉忠[1] 薄彤 LIU Yuzhong;BO Tong(College of Mathematics and Systems Science, Shenyang Normal University, Shenyang 110034, China)

机构地区：[1]沈阳师范大学数学与系统科学学院

出　　处：《沈阳师范大学学报（自然科学版）》2019年第3期193-197,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省科技厅自然科学基金资助项目(20170540823)

摘　　要：主要对一类积分时滞切换系统的指数稳定问题进行研究。首先,在积分时滞系统上加入切换的概念。通过构建出一类特殊的限定时滞上界和下界的Lyapunov-Krasovskii函数的方法来处理积分时滞切换系统的指数稳定性问题。在积分项的处理上,运用了Cauchy-Schwarz不等式以及Jensen不等式进行放缩,使系统得到更小的保守性结果,进而得到积分时滞切换系统的指数稳定性条件。与此同时,利用平均驻留时间的方法,给出了积分时滞切换系统切换律的设计方案,处理了在任意切换下的积分时滞切换系统的指数稳定性。最后,将单时滞积分时滞切换系统的指数稳定性研究推广到带有多时滞的积分时滞切换系统中,使得积分时滞切换系统的指数稳定性研究更具有一般性,从而在控制工程的理论基础方面取得新成果。In this paper, the exponential stability of a class of switched systems with integral delay is studied. For the first time, the concept of switching is added to the integral time-delay system. A special Lyapunov-Krasovskii function with upper and lower bounds of time-delay is constructed to deal with the exponential stability of switched systems with integral time-delay. In the treatment of integral terms, Cauchy-Schwarz inequality and Jansen inequality are used to scale down, so as to obtain smaller conservative results, and finally the exponential stability conditions of switched systems with integral time-delay are obtained. In addition, by using the method of average dwell time, the switching law of switched systems with integral delay is designed, and the exponential stability of switched systems with integral delay under arbitrary switching time is analyzed. Finally, the exponential stability of switched systems with single delay and integral delays is extended to switched systems with multiple delays, which makes the study of exponential stability of switched systems with integral delays more general. Thus, new achievements have been made in the theoretical basis of control engineering.

关 键 词：积分时滞系统 切换系统 指数稳定性 平均驻留时间 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]