Abstract
In this article, we establish the stabilization of a class of second order semi-linear hyperbolic systems obtained by nonlinear feedback using the observability of the corresponding uncontrolable systems. We obtain the well-posedness of the semilinear system by standard argument of Ball ([3]), Our technique of proof relies on an appropriate decomposition of the solution, and the energy method. Our result generalizes an earlier one by Haraux [5] who studied the same type of problem for linear systems, and by Louis Tebou [9] for de case of semi-linear systems. Application of our result are provided.