摘要
线性时滞系统稳定性分析,一直是控制领域研究的热点问题之一.特别是在Wirtinger-based积分不等式提出后,线性时滞系统的稳定性问题掀起了一轮研究热潮.基于不等式的Lyapunov-Krasovskii(L-K)泛函方法得到了迅速发展并逐渐成为研究线性时滞系统稳定性问题的主流方法.本文将主要讨论基于不等式的L-K泛函方法在线性时滞系统稳定性研究中的最新成果.首先,回顾了一些具有代表性的积分不等式和矩阵不等式,并分析了其对减小稳定性条件保守性所起的作用.其次,讨论了最近几年发展起来的具有代表性的L-K泛函.最后,给出了总结并展望了线性时滞系统稳定性研究将来所要解决的一些问题.
Stability analysis of linear time-delay systems is always one of the hottest issues in control research fields.Especially after the establishment of the Wirtinger-based integral inequality,there is an upsurge in stability analysisof linear time-delay systems.The Lyapunov-Krasovskii(L-K)functional method is developing rapidly and has become the main way in studying the stability of time-delay systems.We mainly discuss recent advances of the inequality-based L-K functional method in stability analysis of linear time-delay systems.Firstly,we recall some typical integral and matrix inequalities and analyse their roles in reducing the conservatism of stability conditions.Secondly,we discuss some recently-developed L-K functionals.Finally,some conclusions are made and some problems are presented that need to be solved in the future for the stability of timedelay systems.
作者
陈军
徐胜元
张保勇
CHEN Jun;XU Shengyuan;ZHANG Baoyong(School of Electrical Engineering and Automation,Jiangsu Normal University,Xuzhou 221116,China;School of Automation,Nanjing University of Science and Technology,Nanjing 210094,China)
出处
《信息与控制》
CSCD
北大核心
2020年第1期36-46,共11页
Information and Control
基金
国家自然科学基金资助项目(61773186,61673215,61877030)
江苏师范大学博士学位教师科研支持项目(17XLR045).
关键词
线性时滞系统
L-K泛函
稳定性
积分不等式
linear time-delay system
L-K functional
stability
integral inequality
作者简介
陈军(1978-),男,博士,副教授,硕士生导师,研究领域为T-S模糊系统,时滞系统等;通信作者:徐胜元(1968-),男,博士,教授,博士生导师,研究领域为时滞系统,广义系统,非线性系统等,syxu@njust.edu.cn;张保勇(1981-),男,博士,教授,博士生导师,研究领域为时滞系统鲁棒控制理论。
