EXPONENTIAL STABILITY OF 1-D WAVE EQUATION WITH THE BOUNDARY TIME DELAY BASED ON THE INTERIOR CONTROL

摘要

In this paper, the stability problem of 1-d wave equation with the boundary delay and the interior control is considered. The well-posedness of the closed-loop system is investigated by the linear operator. Based on the idea of Lyapunov functional technology, we give the condition on the relationship between the control parameter α and the delay parameter k to guarantee the exponential stability of the system.