不确定线性时滞系统的一种鲁棒镇定方法  

A Robust Stabilization Method for Uncertain Linear Systems with Time-Delay

作　　者：郑连伟[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2010年第8期1070-1073,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(60774097)

摘　　要：利用Lyapunov泛函方法研究了不确定线性时滞系统的鲁棒镇定问题.不确定性是范数有界的时变矩阵.为了估计Lyapunov泛函的导数,首先建立了两个对称矩阵Schur补之间的一个不等式,据此得到了一个关于不确定二次函数上界的不等式.通过对不确定二次函数的估计和矩阵运算,把Lyapunov泛函导数的负定性转化为线性矩阵不等式的可行性问题,从而得到了系统可以鲁棒镇定的充分条件,同时用线性矩阵不等式的解构造了鲁棒状态反馈控制器的增益矩阵.数值算例表明,这种鲁棒镇定方法具有较小的保守性.The robust stabilization for uncertain linear systems with time-delay is investigated by Lyapunov functional approach.The uncertainties are assumed to be norm-bounded and time-varying matrices.An inequality between Schur complements of two symmetric matrices is established.Then,an inequality for the upper bound of uncertain quadratic functions is obtained to estimate the Lyapunov functional derivative.Estimating the uncertain quadratic functions and performing some matrix manipulation,the negativity of Lyapunov functional is converted into a feasibility problem of linear matrix inequalities,thus giving a sufficient condition for robust stabilization.Meanwhile,the gain matrix of a robust state feedback controller is constructed via the solutions of the linear matrix inequalities.Numerical examples showed the robust stabilization method obtained in this way is less conservative.

关 键 词：时滞系统 鲁棒镇定 LYAPUNOV泛函 线性矩阵不等式 不确定性 SCHUR补 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]