不确定性离散时间线性系统的鲁棒脉冲镇定  

Robust Impulsive Stabilization of Uncertain Linear Discrete-Time Systems

作　　者：柳长青[1] 陈武华[2,3] LIU Chang-qing;CHEN Wu-hua(Department of Mathematics and Computer Information Engineering,Baise University,Baise 533000,China;College of Mathematics and Information Science,Guangxi University,Nanning 530004,China;Laboratory of Guangxi Electric Power System Optimization and Energy-saving Technology,Nanning 530004,China)

机构地区：[1]百色学院数学与计算机信息工程系,广西百色533000 [2]广西大学数学与信息科学学院,广西南宁530004 [3]广西电力系统最优化与节能技术重点实验室,广西南宁530004

出　　处：《数学的实践与认识》2019年第18期140-146,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11661001,61573111);广西自然科学基金重点项目(2018JJD170015);广西高校科学技术研究项目(KY2015YB280)

摘　　要：针对具有范数有界不确定性的线性离散时间系统,研究了鲁棒状态反馈脉冲镇定问题.首先,引入与脉冲时间序列相关的时变Lyapunov函数,运用凸组合技术,给出一种能够保证闭环系统鲁棒指数稳定性的状态反馈脉冲控制律存在的充分条件;其次,证明了该条件可转化为一组线性矩阵不等式可解性问题.通过求解这组线性矩阵不等式,可以获得鲁棒状态反馈脉冲控制律增益矩阵;最后,通过数值例子说明所得结果的有效性.The robust impulsive stabilization problem of uncertain linear discrete-time systems is considered.The uncertainties are time-varying but norm bounded.Firstly,a timevarying Lyapunov function associated with the impulse time sequence is introduced.By applying the technique of convex combination,a sufficient condition for the existence of state feedback impulsive control law that ensures exponential stability of the closed-loop system is presented.Then,it is shown that this condition can be converted into the solvability problem of a set of linear matrix inequalities.By solving a set of linear matrix inequalities,the feedback gain matrices of robust impulsive control law can be obtained.Finally,a numerical example is presented to illustrate the efficiency of the proposed method.

关 键 词：鲁棒指数稳定 离散时间系统 时变Lyapunov函数 不确定 

分 类 号：O175[理学—数学] TP13[理学—基础数学]