On the finite-time stabilization of strings connected by point mass

Abstract

In this paper, the problem of finite-time boundary stabilization of two strings connected by point mass is investigated. Based on the so-called Riemann invariant transformation, the vibrating strings are transformed in two hybridhyperbolic systems, and leads to the posedness of our system. In order to act in the system, it is desirable to choose boundary feedbacks, in this case, Holderien stabilizing feedback laws to vanish in finite-time the right and the left of the solutions are considered.