一类切换时滞系统的增长无源性  

Incremental passivity for a class of switched time-delay systems

作　　者：李莉莉[1] 刘晨 罗静文 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《沈阳师范大学学报（自然科学版）》2017年第4期415-418,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(61304056;11671184);大连市高层次人才创新支持计划项目(2016RQ049)

摘　　要：无源性是描述系统输入输出关系的重要性质,增长无源性是无源性的一种推广形式。受时滞系统无源性和非时滞系统的增长无源性的启发,提出一类切换时滞系统的增长无源性定义。基于多李雅普诺夫函数方法,设计依赖于状态的切换规则,Wirtinger积分不等式与Finsler引理相结合用于处理系统中的时滞项,以线性矩阵不等式的形式给出切换时滞系统具有增长无源性的充分条件。特别地,当参数取特殊值时,讨论了切换时滞系统具有输入增长无源性和输出增长无源性的充分条件。作为詹森积分不等式的拓广形式,在处理时滞项时选取Wirtinger积分不等式有助于降低所得结果的保守性。Passivity is an important property to describe the relation between the system input and output,and the incremental passivity is a generalization type of the passivity.Inspired by the passivity of time-delay systems and the incremental passivity of non-time-delay systems,this paper proposes the definition of the incremental passivity for a class of switched time-delay systems.Based on the multiple Lyapunov function method,switching rules dependent on the system state is designed,and the Wirtinger integral inequality and Finsler Lemma are combined to deal with the delay terms in the systems,sufficient conditions for the incremental passivity of the switched time-delay systems are given in the form of linear matrix inequalities.In particular,when parameters take some special values,the sufficient conditions for the incremental input passivity and the incremental output passivity of the systems are discussed meanwhile.As the extension form of Jensen integral inequality,the Wirtinger integral inequality which is chosen to deal with the delay terms is helpful to reduce the conservativeness of the proposed results.

关 键 词：切换时滞系统 增长无源性 多李雅普诺夫函数 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]