时滞不确定系统研究综述

Survey of Uncertain Time-delay Systems

时滞广泛存在于工程实践中,时滞往往是引起系统不稳定甚至导致系统性能恶化的重要因素之一,并且时滞的存在给系统的稳定性分析及控制器设计都带来了很大的困难.在过去30年中,控制界对时滞系统的分析、综合和控制的研究兴趣不断提高.主要介绍利用Lyapunov稳定性定理和线性矩阵不等式工具给出的时滞相关的渐近稳定性和控制的充分条件.构造新的Lyapunov-Krasovskii泛函,基于线性矩阵不等式和自由权矩阵方法得到保守性低的结果是近年学者们的主要研究工作.时滞系统的研究面临很多挑战,但它必将具有广阔的理论和应用前景.最后,简单指出了今后的研究方向.

Time-delay widely exists in the field of science and engineering. It＇s often an important factor of instability or performance deterioration in those systems. Besides, its existence brings great difficulties in stability analysis and controller design of the system. During the last three decades, there has been an increasing interest in the analysis, synthesis and control of time-delay systems. The purpose of this paper is to give an overview on the current development of the research on time-delay systems. The paper puts forward sufficient conditions for asymptotic stability and control based on Lyapunov-function and linear matrix inequalifies（LMIs）, as weli as the use of new Lyapunov Krasovskii functional. The less conservative conditions based on LMIs and free weighting matrices method is scholars＇ main research interests recently. Though there are many challenges for the research of the time-delay systems, the excellent theory and applications are anticipated. Further research directions are also presented.