基于增广Lyapunov泛函的时滞系统鲁棒H_∞控制  

Robust H_∞ Control for Time-Delay Systems Based on Augmented Lyapunov Functionals

作　　者：李圣涛[1] 井元伟[1] 刘小梅[2] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819 [2]东南大学自动化学院,江苏南京210096

出　　处：《东北大学学报（自然科学版）》2012年第1期21-24,34,共5页Journal of Northeastern University(Natural Science)

基　　金：国家高技术研究发展计划项目(2010AA101702)

摘　　要：研究了一类时滞系统的鲁棒H∞控制问题.利用增广Lyapunov泛函并结合自由权矩阵方法,以严格线性矩阵不等式(LMIs)的形式给出了保证闭环系统渐近稳定且具有给定H∞性能的改进的时滞相关有界实引理(BRL).基于得到的BRL,以LMIs的可行解给出了记忆型的状态反馈H∞控制律.当时滞系统存在范数有界不确定性时,同样地给出了基于LMIs的记忆型鲁棒H∞控制律的具体设计方法.仿真实例表明了该方法的有效性以及更小保守性.The problem of delay-dependent robust H∞ control for systems with state-delay was investigated. An improved delay-dependent bounded real lemma （BRL） was established in terms of linear matrix inequalities （LMIs） by using augmented Lyapunov functionals and free-weighting matrices method, ensuring the resultant closed-loop system asymptotically stable and a prescribed H∞ performance level. Based on the obtained BRL, the state feedback H∞ control law with memory was given in terms of the feasible solutions of LMIs. When the time-varying norm- bounded uncertainties appeared in a time-delay system, the explicit design approach of the robust H∞ controller was also given and formulated in the form of LMIs. Numerical examples are provided to demonstrate the reduced conservatism and validity of the proposed conditions.

关 键 词：时滞系统 H∞控制 时滞相关 线性矩阵不等式(LMIs) 有界实引理 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]