具有边界输入时滞的一维波方程的稳定性  

Stability of One-dimensional Wave Equations with Boundary Input Delays

作　　者：王小瑞[1] WANG Xiao-rui(Department of Mathematics and Statistics,Qinghai Nationalities University,Xining 810007,China)

机构地区：[1]青海民族大学数学与统计学院,青海西宁810007

出　　处：《兰州文理学院学报（自然科学版）》2018年第6期6-10,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：青海省自然科学基金(2017-ZJ-908);青海民族大学校级青年项目(2017XJQ06)

摘　　要：研究了边界具有输入时滞的一维波方程的指数稳定性.首先,采用Smith预估器方法设计了状态反馈控制律,进而得到了相应的闭环系统;其次,利用算子的可容许理论证明了闭环系统的适定性;最后,使用李雅普诺夫方法证明了系统的指数稳定性.In this paper,the exponential stability of one-dimensional wave equations with input delays on the boundary is studied.Firstly,the state feedback control law is designed by using the Smith predictor method,and then the corresponding closed-loop system is obtained.Secondly,the appropriateness of the closed-loop system is proved by using the admissibility theory of operators.Finally,the exponential stability of the system is proved by the Lyapunov method.

关 键 词：波方程 输入时滞 反馈控制器 指数稳定 

分 类 号：O231.4[理学—运筹学与控制论]