线性时滞中立型系统的周期间歇镇定  

Periodical Intermittent Stabilization of Linear Neutral-Type Systems with Delay

作　　者：蒋燕[1] 刘琼[2] 

机构地区：[1]广西大学数学与信息科学学院,广西南宁530004 [2]钦州学院数学与计算机科学学院,广西钦州535000

出　　处：《广西科学》2015年第4期438-444,共7页Guangxi Sciences

基　　金：广西高校科研项目:广西研究生教育创新计划项目(YCSZ2015031);半连续动力系统几何理论及其害虫综合治理研究项目(ZD2014137);钦州学院"专业综合改革试点项目":数学与应用数学(2012QZZYSD05)资助

摘　　要：首先,通过变量替换将原问题转化为一类奇异系统的间歇镇定问题;其次,基于间歇控制系统具有切换系统的动态特性,引入与控制周期、控制宽度相关的时变切换Lyapunov泛函,运用凸组合技术,给出系统稳定性的充分条件;再次,证明该条件可以转化为一组线性矩阵不等式的可行解问题.通过求解该组线性矩阵不等式,获得间歇控制增益矩阵;最后,通过数值例子验证本文所用方法的有效性.较时不变Lyapunov泛函方法,本文所提出的时变切换Lyapunov泛函方法能有效地利用系统的动态特性,避免结果的局限性.Firstly,by introducing variable substitution,the original problem is transformed into the periodically intermittent stabilization problem of a class of singular system.Next,a time-varying switched Lyapunov functional associated with the control period and the control width is introduced,based on the dynamic characteristics of switched system which is contained in the periodic intermittent control system.A sufficient condition of stabilization of the system can be obtained by using the convex combination technique.This condition can be converted into the solvability problem of a set of linear matrix inequalities.The intermittent control gain matrix can be obtained by solving a set of linear matrix inequalities.Finally,the validity of the proposed method is presented through a numerical example.Compared with the time-invariant Lyapunov functional based methods,the proposed time-varying switched Lyapunov functional method can effectively utilize the dynamic characteristics of the considered system.Thus,the conservatives of the results can be reduced.

关 键 词：中立型系统 间歇控制 时变Lyapunov泛函 线性矩阵不等式 全局指数稳定 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]