不确定离散系统的鲁棒非脆弱H_∞控制  

Robust and Non-fragile H_∞ Control for Discrete-time Uncertain Linear Systems

作　　者：王武[1] 杨富文[1] 

机构地区：[1]福州大学电气工程与自动化学院,福建福州350002

出　　处：《控制工程》2005年第4期335-338,共4页Control Engineering of China

基　　金：福建省自然科学基金资助项目(A0410012);福建省教育厅科技基金资助项目(JB04004);福州大学人才基金资助项目(2004-XJY-0401)

摘　　要：针对线性不确定离散系统,研究了鲁棒非脆弱H∞状态反馈控制器的设计问题。鲁棒性是研究被控系统模型参数摄动对闭环系统的影响,脆弱性是研究控制器参数摄动对闭环系统的影响。在系统模型和控制器同时存在不确定时,只有鲁棒非脆弱的控制器才能保证闭环系统的稳定和满足给定性能。系统的不确定项参数时变且具有线性分式形式的范数有界,控制器的增益变化也是时变且具有线性分式形式的范数有界。基于线性矩阵不等式方法,给出了具有加性和乘性控制器增益变化的鲁棒非脆弱控制器存在的充要条件。实例表明了该设计方法的有效性。The problem of robust and non-fragile H_∞ control via state feedback for linear discrete-time uncertain systems is studied.While robustness relates to uncertainties in the mathematical model of a controlled system,fragility relates to the uncertainties in the implementation of a designed controller.When both controlled system and controller have uncertainties,no other than the robust and non-fragile controller can stabilize the closed-loop systems and guarantee a prescribed performance.The systems are assumed to have norm-bounded parameter uncertainties.The controller gains are assumed to have norm-bounded parameter uncertainties which can be either additive or multiplicative.The necessary and sufficient condition for the existence of robust and non-fragile controller is presented via linear matrix inequality (LMI).A numerical example shows the validity of the design method.

关 键 词：非脆弱控制 鲁棒H∞状态反馈 不确定系统 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]