一种改进的区间时变时滞系统稳定性准则  

An Improve Stability Criterion for Systems with Interval Time-varying Delay

作　　者：尹宗明 张宁 雷蔓 仇磊 YIN Zong-ming;ZHANG Ning;LEI Man;QIU Lei(School of Mechanical Engineering,Guizhou University of Engineering Science,Guizhou 551700,China)

机构地区：[1]贵州工程应用技术学院机械工程学院,贵州毕节551700

出　　处：《控制工程》2020年第3期462-468,共7页Control Engineering of China

基　　金：贵州省教育厅科技合作计划项目(黔科合LH字[2016]7063号);贵州省教育厅青年科技人才成长项目(黔教合KY字[2016]228).

摘　　要：研究区间时变时滞系统的稳定性问题。首先,通过引入一个区间调节参数,将系统时滞区间分解为两部分之和。其次,在两个子区间的基础上构造一个包含更多时滞信息和三重积分项的新Lyapunov-Krasovskii (L-K)泛函。在处理来自L-K泛函求导过程中产生的积分交叉项时,将时滞分属于各子区间的情况作为一个整体来研究。然后,基于Lyapunov稳定性理论,以线性矩阵不等式的形式给出一个新的稳定性准则。最后,通过两个数例证明所得稳定性准则的有效性。The problem of stability for systems with interval time-varying delay is concerned in this paper. Firstly, the delay interval of systems is decomposed into two sub-intervals by introducing an interval adjusting parameter. Secondly, on the basis of each sub-interval, a new Lyapunov-Krasovskii(L-K) functional, which includes more information of delay and some new triple-integral terms, is constructed. In the process of dealing with the integral cross terms from the derivation of L-K functional, the case of time-varying delay falling, respectively, into each sub-interval are lumped into an unit to study. Thirdly, based on Lyapunov stability theory, a new delay-dependent stability criterion is proposed in the form of linear matrix inequalities. Finally, the effectiveness of the proposed stability criterion is demonstrated via two examples.

关 键 词：稳定性准则 时滞分解 区间时变时滞 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]