不确定时滞系统新的鲁棒镇定方法  

New Robust Stabilization Method for Uncertain Systems with Delays

作　　者：刘继清[1] 黄金花[1] 

机构地区：[1]武汉船舶职业技术学院电子电气工程系,湖北武汉430050

出　　处：《武汉理工大学学报（信息与管理工程版）》2011年第1期43-46,共4页Journal of Wuhan University of Technology：Information & Management Engineering

基　　金：国家自然科学基金资助项目(60974012)

摘　　要：研究了一类不确定时滞线性系统的镇定问题。所考虑的系统是由状态方程来描述的,且其中的不确定参数是时变未知但范数有界的。首先通过解一个Riccatti方程给出了相应镇定控制器的设计方法。其次,由Riccatti方程的解得到了一个二次Lyapunov-Krasovskii泛函,以确保相应闭环系统的渐近稳定性,由此给出了线性系统"二次可镇定"的定义。同时,通过线性矩阵不等式给出了具有时滞独立的线性系统稳定的相关判据,并在此基础上得出了相应的状态反馈控制器,保证了相应闭环系统的鲁棒稳定性。最后,通过一个数值例子说明了该方法的有效性。The stabilization of a class of uncertain linear systems with time-delay was presented.The uncertain systems under consideration were described by state equations which depended on time-varying unknown-but-bounded uncertain parameters.Firstly,the construction of the stabilizing controller involved in solving a certain algebraic Riccati equation.Secondly,the solution to this Riccati equation defined a quadratic Lyapunov-Krasovskii functional which was used to establish the stability of the closed-loop system.This led to a notion of ＂quadratic stabilizability＂.Some delay-independent stability criterions were derived in terms of linear matrix inequalities to ensure that the nominal system was stable.Based on these criterions,the problem was solved via state feedback controller,guaranteeing the resultant closed-loop system is robustly stable.Finally,a numerical example was given to illustrate the effectiveness of the proposed method.

关 键 词：状态反馈 镇定 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] O231[自动化与计算机技术—控制科学与工程]