On the finite-time Bhat-Bernstein feedbacks for the strings connected by point mass

Abstract

In this article, the problem of finite-time stabilization of two strings connected by point mass is discussed. We use the so-called Riemann coordinates to convert the study system into four transport equations coupled with the dynamic of the charge. We act by Bhat-Bernstein feedbacks in various positions (two extremities, the point mass and one of boundaries, only on the point mass,...) and we show that in some cases the nature of the stability depends sensitively on the physical parameters of the system.

Some results on the internal finite‐time stabilization of vibrating strings with interior mass

“…As application, we have proved that waves produced by the motion of strings connected by point mass disappear in finite-time. In Belgacem et al, 23,24 the problem of boundary stabilization of (1)-(7) is reconsidered in finite-time. More precisely, boundary feedbacks that conduct to the dissipation of the system energy in finite-time are established.…”