Stabilization of the wave equation with interior input delay and mixed Neumann-Dirichlet boundary

Abstract

This paper considers the stabilization of a wave equationwith interior input delay: $\mu_1u(x,t)+\mu_2u(x,t-\tau)$,where $u(x,t)$ is the control input. A new dynamic feedbackcontrol law is obtained to stabilize the closed-loop systemexponentially for any time delay $\tau>0$ provided that$|\mu_1|\neq|\mu_2|$. Moreover, some sufficient conditionsare given for discriminating the asymptotic stabilityand instability of the closed-loop system.