具有饱和执行器的不确定脉冲系统的鲁棒镇定  

Robust stabilization of uncertain impulsive systems with saturating actuator

作　　者：黎艳[1] 陈武华[2,3] 

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：《西北师范大学学报（自然科学版）》2013年第6期10-15,25,共7页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(61164016);广西自然科学基金重点项目(2013GXNSFDA019003);广西自然科学基金资助项目(2011GXNSFA018141)

摘　　要：针对一类具有饱和执行器的不确定脉冲系统,研究了鲁棒线性反馈镇定及其吸引域估计问题.首先,对给定的状态反馈控制律,引入与脉冲时间序列关联的Lyapunov函数,并结合饱和函数的凸包表示,给出了零解鲁棒指数稳定性以及零解吸引域与脉冲区间长度的关系.然后,引入凸参考集,基于线性矩阵不等式,将求解使系统可鲁棒镇定的最大吸引域估计问题转化为凸优化问题.在脉冲区间上界信息已知的情形,本文结果改进了现有的结果.数值例子验证了本文方法的有效性和优越性.Although many effective methods for robust control of uncertain dynamical systems with saturating actuators have been reported in the literatures , there are only a few results having taken into account of the effect of impulses on controller design and estimation of domain of attraction . The impulse disturbances degrade the system performance and increase the difficulties of system analysis . Therefore , it is of great importance to study the robust control problem of uncertain systems with input saturation under impulse disturbances . T he purpose of this paper is to investigate the problems of robust linear feedback stabilization and estimation of domain of attraction for a class of uncertain impulsive systems with saturating actuator . First , for a prescribed state feedback control law , by introducing a Lyapunov function associated with the impulse time sequence and by using the convex hull based representation of the saturation function , the relationship between the length of impulsive intervals and robust exponential stability and domain of attraction is built . T hen , by introducing the convex reference sets and by using the techniques of linear matrix inequalities , the problem of finding the largest estimation of domain of attraction such that the system can be robustly stable is transferred to a convex optimization problem . In the case that the knowledge of upper bound of impulsive intervals is known , the proposed results improve the existing ones . A numerical example is presented to show the validity and superiority of the derived results .

关 键 词：脉冲系统 饱和执行器 鲁棒镇定 吸引域 

分 类 号：O231.2[理学—运筹学与控制论]