不确定时变时滞系统的鲁棒最优H_∞控制  

Robust H_∞ optimal control for uncertain time-varying delay systems

作　　者：杨瑞珍[1] 包俊东[1] 

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《南京信息工程大学学报（自然科学版）》2010年第1期62-67,共6页Journal of Nanjing University of Information Science & Technology（Natural Science Edition）

基　　金：内蒙古自然科学基金(200711020104)

摘　　要：针对一类参数不确定时变时滞线性系统,研究了鲁棒最优H∞控制器的设计问题.首先利用积分不等式和引入自由权矩阵的方法,得到了系统稳定及H∞反馈控制器存在的充分条件;然后将其转化为线性矩阵不等式(LMI)表示,通过线性矩阵不等式的可行解构造控制器,保证了闭环系统渐近稳定且满足一定的H∞干扰抑制水平,得到的稳定化条件是依赖时滞大小且不要求时滞函数的导数信息,即适用于时滞快速变化的系统.算例表明了该方法的可行性.The problem of robust H∞ controller design is studied for uncertain time-varying linear systems with time-delay. A sufficient condition of existence of H∞ feedback controller is obtained by using integral inequality and free-weighting matrix method. Then the sufficient condition is transformed to a linear matrix inequality （LMI） presentation. The controller is easily constructed by the feasible solution of the LMI. The obtained controller guarantees the robust stability and a prescribed H∞ performance of the closed-loop system. The stabilization condition depends on the size of delay but requires no information about the derivate of time delay,which is applicable to the systems with fast time-varying delay. The example shows the feasibility of the approach.

关 键 词：鲁棒H∞控制 不确定系统 时滞依赖 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]