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

A new dynamic feedback control law can stabilize a closed-loop system exponentially with interior input delay, providing sufficient conditions for discriminating between asymptotic stability and instability.

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

Key Takeaway: A new dynamic feedback control law can stabilize a closed-loop system exponentially with interior input delay, providing sufficient conditions for discriminating between asymptotic stability and instability.