Novel Stability Criteria for Linear Time-Delay Systems Using Lyapunov-Krasovskii Functionals With A Cubic Polynomial on Time-Varying Delay  

作　　者：Xian-Ming Zhang Qing-Long Han Xiaohua Ge 

机构地区：[1]the School of Software and Electrical Engineering,Swinburne University of Technology,Melbourne,VIC 3122,Australia

出　　处：《IEEE/CAA Journal of Automatica Sinica》2021年第1期77-85,共9页自动化学报（英文版）

基　　金：supported in part by the Australian Research Council Discovery Project(Grant No.DP160103567)。

摘　　要：One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

关 键 词：Bessel-Legendre inequality matrix-valued polynomial inequalities stability time-varying delay time-delay systems 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]