Stabilization of wave equations with boundary delays and non-collocated feedback controls

摘要

This paper deals with the non-collocated, time-delayed actively point controls of a star-shaped network modeled by wave equations which has a rigid body attached on the common vertex. A closed-loop control is provided. It is shown that the closed-loop system is exponential stable if and only if it is asymptotically stable and there are at most finite eigenvalues on the imaginary axis under certain conditions. Furthermore, the exponential stability of the closed-loop system can always be obtained by choosing suitable feedback gain constants.