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

Abstract

In this paper, the problem of internal finite-time stabilization for 1-D coupled wave equations with interior point mass is handled. The nonlinear stabilizing feedback law leads, in closed-loop, to nonlinear evolution equations where Kato theory is used to prove the well-posedness. In addition, it is showed that in some cases, the solution of this hybrid system is constant in finite-time if we use Neumann boundary conditions. This result can be improved (in complete finite-time stability sense) if we change the above feedback.