一类区间时变时滞切换系统的稳定性  

Stability of a class of switched systems with interval timevarying delays

作　　者：刘玉忠[1] 佟雪 LIU Yuzhong;TONG Xue(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,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2018年第3期226-232,共7页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61703290)

摘　　要：研究一类具有区间时变时滞线性切换系统的稳定性问题,通过构造一类限定时滞上下界的分段Lyapunov-Krasovskii(L-K)函数并结合线性矩阵不等式(LMI)技术建立一种新的稳定性判据。首先,基于时滞分割法将时滞区间平均分割成n等分,在每一段子区间上构造带有三重积分形式的L-K泛函;其次,应用保守性更小的Jenson不等式以及一阶、二阶倒数凸组合技术处理L-K泛函沿着时间导数中的积分项,得到具有区间时变时滞的线性切换系统稳定性的充分条件;最后,将具有区间时变时滞的线性切换系统稳定性问题归结为LMI的求解问题,这样便于利用Matlab工具箱求解并验证结论的有效性。This paper studies the stability of linear switched systems with interval time-varying delays by constructing a kind of piecewise Lyapunov-Krasovskii functions which limit the upper and lower bounds of delays.Combined with linear matrix inequality（LMI）,a new stability criterion is established.Based on the delay-partitioning approach,the time-delay interval is divided into n equal parts,and the L-K function with triple integral form will be constructed on each sub-interval.By using the less conservative Jenson inequalities and the first-order and second-order reciprocal convex combination techniques to deal with the integrals of the L-K function along the time derivative.We gain the sufficient conditions for the stability of linear switched systems with interval time-varying delays.Finally,the problem of stability of linear switched systems with interval time-varying delays can be solved by LMI technique,which is convenient to solve and prove the validity of conclusion by using the tool box of Matlab.

关 键 词：二阶倒数凸组合方法 区间时变时滞 时滞分割法 稳定性分析 三重积分形式 L-K泛函 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]