一类不确定线性时变时滞系统的鲁棒H∞控制  

Robust H∞ Controller Design for a Class of Uncertain Linear Systems with Time-varying and Control Delay

作　　者：屈百达 张玉军 廖建庆[1,2] 

机构地区：[1]江南大学轻工过程先进控制教育部重点实验室,江苏无锡214122 [2]宁德师范学院物理与电气工程系,福建宁德352100

出　　处：《控制工程》2016年第1期91-96,共6页Control Engineering of China

基　　金：高等学校学科创新引智计划资助(B12018);江苏高校优势学科建设工程资助项目;江苏省产学研联合创新资金项目(120767);福建省自然科学基金项目(2015J01661)

摘　　要：主要研究一类同时具有时变状态时滞和控制时滞不确定线性系统的鲁棒H∞控制。通过构造带有时滞上下界信息的Lyapunov-Krasovskii函数,在估计其导数上界时把时变时滞和它的上下界之间的关系考虑进去,结合一种由引入自由权矩阵的Park不等式导出了新的二次型积分不等式的方法,得到了一类自治系统的时滞依赖条件并在此基础上设计了H∞控制器。最后用数值算例表明了该时滞系统与状态反馈律所组成的闭环系统具有较好的H∞性能和较低的保守性。Robust Hoocontroller design for a class of uncertain linear delay systems with time-varying and control delay has been studied in this paper, based on Lyapunov stability theory and linear matrix inequality. By constructing a Lyapunov-Krasovskii function based on the upper and lower bound time-delay information, the upper bound of its derivative is estimated considering the relationship between the time-varying delay and its upper and lower bounds, then combining with the new quadratic integral inequality derived by Park inequality which has introduced the freedom matrix to get delay-dependent conditions of a class of autonomous systems,a the robust Hoocontrol law is further designed. Finally, a numerical example is given to illustrate the better performance and less conservativeness of the closed-loop system consisting of delay system and state feedback law.

关 键 词：不确定时变时滞系统 鲁棒H∞控制器 二次型积分不等式 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]