中文摘要：

这份报纸与一个不稳定的边界条件，观察在服从于任意的确定的时间延期集中于一个一个维的波浪方程的边界稳定。observability 不平等显示开环的系统是看得见的，基于哪个观察员和预言者被设计：系统的状态与可得到的观察被估计然后没有观察，预言了。在那以后，相等地，作者由 backstepping 方法转变原来的系统到提出得好、指数地稳定的系统。和观察员和预言者的设计的相等的系统给估计的产量反馈。靠近环的系统是指数地稳定的，这被显示出。数字模拟被介绍说明稳定的控制器的效果。

英文摘要：

This paper focuses on boundary stabilization of a one-dimensional wave equation with an unstable boundary condition,in which observations are subject to arbitrary fixed time delay.The observability inequality indicates that the open-loop system is observable,based on which the observer and predictor are designed：The state of system is estimated with available observation and then predicted without observation.After that equivalently the authors transform the original system to the well-posed and exponentially stable system by backstepping method.The equivalent system together with the design of observer and predictor give the estimated output feedback.It is shown that the closed-loop system is exponentially stable.Numerical simulations are presented to illustrate the effect of the stabilizing controller.