不确定变时滞中立型系统的指数稳定H_∞控制  

Exponential Stable H_∞ Control for Uncertain Neutral Systems with Time-varying Delays

作　　者：杨晓光[1] 于丽丽[1] 孟垂茁[1] 

机构地区：[1]大连海事大学数学系,辽宁大连116026

出　　处：《控制工程》2008年第5期514-518,共5页Control Engineering of China

基　　金：国家自然科学基金资助项目(60575039)

摘　　要：针对一类不确定变时滞中立型系统,基于Lyapunov稳定性理论,采用线性矩阵不等式(LMI)处理方法,研究了其指数稳定H∞控制问题。对所有参数不确定性和时变时滞性,设计线性无记忆状态反馈控制器,使得闭环系统是指数稳定的且满足给定的H∞性能指标。首先讨论无扰动闭环系统的指数稳定性,在此基础上,得到了系统具有H∞性能指标的充分条件。并将其转化为线性矩阵不等式的形式,从而可以很方便地利用Matlab工具箱进行求解。最后给出算例验证结论的有效性。Based on the Lyapunov stability theory and the linear matrix inequality （LMI）approach, the problem of the exponentially stable H∞ control for a class of uncertain neutral systems with time-varying delays is considered. The purpose is to design a linear memoryless state feedback controller so that the closed-loop system is exponentially stable and satisfies H∞ performance index for all admissible uncertainties and time-varying delays. The exponential stability of the closed-loop system without disturbance is considered. Based on that, a sufficient condition for the system with H∞ property is obtained and shown by a certain LMI. It can be easily solved by Matlab toolbox. Numerical example shows the effectiveness of the proposed method.

关 键 词：中立型时滞系统 指数稳定性 线性矩阵不等式 LYAPUNOV稳定性 H∞控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]