一类区间时滞切换系统的稳定性分析  

Stability analysis of a class of interval switched systems with time delay

作　　者：刘玉忠[1] 吴得渤 LIU Yuzhong;WU Debo(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）》2022年第1期30-34,共5页Journal of Shenyang Normal University:Natural Science Edition

基　　金：辽宁省教育厅科学研究经费项目(LJC202002)。

摘　　要：在过去的几十年里,具有离散和分布时滞的混合系统受到很多关注,并有着广泛应用,如绝对稳定控制,非线性延迟MIMO系统周期控制T不变性等。有关切换系统的研究中,稳定性问题引起较多关注,因而,研究具有混合时滞的切换系统稳定性有着重要意义。讨论了一类具有离散和分布时滞的切换系统指数稳定问题。首先,运用平均驻留时间法构造分段Lyapunov函数和切换规则;其次,引入倒凸组合技术和Jensen积分不等式对求导后的分段Lyapunov函数进行放缩,得出系统指数稳定的充分条件;最后,利用LMI工具箱实现仿真算例验证了定理的有效性,得到保守性更小的时滞上界。In the past few decades,hybrid systems with discrete and distributed time delays have received widespread attention and widely used,such as absolute stability control,nonlinear delay MIMO system period control T invariance,etc.Stability issues have received more attention in the study of switching systems,therefore it is of great significance to study the stability of switched systems with mixed time delays.The exponential stability of hybrid switching systems is discussed.Firstly,the piecewise Lyapunov function and switching rule are constructed,and the average residence time method is used;secondly,the inverted convex combination technique and Jensen integral inequality are introduced to scale the derived piecewise Lyapunov function,and the sufficient conditions for the exponential stability of the system are obtained;finally,the validity of the theorem is verified by using the LMI toolbox to implement a simulation example,and the upper bound of the time delay with less conservativeness is obtained.

关 键 词：切换系统 平均驻留时间 倒凸组合 Jensen积分不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]