线性中立型时滞系统的可达集的椭圆形边界(英文)  

Ellipsoidal Bound of Reachable Sets for Linear Neutral Delay Systems

作　　者：刘龙[1] 李明[2] 于海姝[1] 

机构地区：[1]黑龙江科技学院理学院,黑龙江哈尔滨150027 [2]哈尔滨工程大学理学院,黑龙江哈尔滨150001

出　　处：《四川师范大学学报（自然科学版）》2013年第4期563-566,共4页Journal of Sichuan Normal University（Natural Science）

基　　金：supported by Heilongjiang Educational Science Fundation(12521468)~~

摘　　要：可达集是界定带有扰动的系统的状态轨迹的集合.可达集的椭圆型边界可以用来设计带有扰动的可控系统.研究了带有有界峰值扰动的线性中立型时滞系统的可达集的椭圆形边界问题,考虑的延时是时变的,但满足一定的约束.基于改进的Lyapunov-Krasovskii型泛函,依据Lyapunov-Krasovskii稳定性定理,得到了只含有一个标量的以矩阵不等式表示的时滞相关的结论,而且当固定此标量参数时,所得结论就以线性矩阵不等式的形式给出.最后,用一个算例验证了所得结论的可行性.特别地,带有饱和的执行器的线性系统的可达集的椭圆型边界越小,就可以允许更大的控制器增益矩阵,这就会使系统具有更好的性能.The reachable set is a set which bounds the state trajectories for systems with disturbances.The bounding of reachable sets by an ellipsoid is needed to design a controlled system having disturbances.We develop the problem of finding an ellipsoidal reachable set that bounds the states of linear neutral delay systems with bounded peak disturbances.The considered time-delay is time-varying but it has a upper bound in magnitude and rate.Based on the improved Lyapunov-Krasovskii type functional and according to Lyapunov-Krasovskii Theorem,the derived result is a delay-dependent one which is expressed in the form of matrix inequalities containing only one nonconvex scalar parameter,and it becomes an LMI by fixing a scalar parameter.Finally,we show the usefulness of our result by a numerical example.In particular,a smaller ellipsoidal bound of a reachable set for linear systems with saturating actuators permits a larger control gain,and this results in a better performance of the system.

关 键 词：可达集 中立型时滞系统 Lyapunov-Krasovskii型泛函 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]