不确定Lur'e系统的鲁棒脉冲饱和镇定  

Robust Impulsive Saturated Stabilization of Uncertain Lur'E Systems

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：《数学的实践与认识》2015年第6期220-229,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61164016);广西自然科学基金重点项目(2013GXNSFDA019003);广西自然科学基金(2011GXNSFA018141);广西高校科学技术研究立项项目(LX2014402);百色学院科学研究项目(2013KB05)

摘　　要：对一类参数不确定的Lur'e系统,提出了具有饱和执行器的脉冲镇定问题.将饱和非线性项表示为有限个线性函数的凸组合,运用与脉冲时间序列关联的时变Lyapunov函数,建立了具有饱和脉冲输入的不确定Lur'e系统指数稳定性的判据,并获得了零解吸引域的估计.然后,基于线性矩阵不等式,给出了脉冲饱和控制器存在的条件,同时给出了求解最大吸引域估计的凸优化问题.最后,数值实例验证了所提出方法的有效性.The impulsive saturated stabilization problem for a class of Lur＇e systems with uncertain parameters is proposed.By expressing the saturated nonlinear term as the convex combination of finite linear functions,a time-varying Lyapunov function associated with the impulse time sequence is introduced as a means for establishing exponential stability of uncertain Lur＇e systems with saturated impulsive input.An estimation of domain of attraction of zero solution is derived.Then,based on linear matrix inequalities,a sufficient condition for the existence of impulsive saturated controllers is presented.The convex optimization problem for the largest estimation of domain of attraction is also presented.Finally,a numerical example is given to prove the validity of the proposed method.

关 键 词：脉冲控制 Lur'e系统 时变Lyapunov函数 饱和执行器 吸引域 

分 类 号：O231[理学—运筹学与控制论]