On the stabilization and stability robustness against small delays of some damped wave equations

In this paper we consider a system which can be modeled by two different one-dimensional damped wave equations in a bounded domain, both parameterized by a nonnegative damping constant. We assume that the system is axed at one end and is controlled by a boundary controller at the other end. We consider two problems, namely the stabilization and the stability robustness of the closed-loop system against arbitrary small time delays in the feedback loop. We propose a class of dynamic boundary controllers and show that these controllers solve the stabilization problem when the damping coefficient is nonnegative and the stability robustness problem when the damping coefficient is strictly positive