  In this paper, we study the boundary feedback stabilization of a quasilinear
hyperbolic system with partially dissipative structure. Thanks to this
structure, we construct a suitable Lyapunov function which leads to the
exponential stability to the equilibrium of the $H^2$ solution. As an
application, we also obtain the feedback stabilization for the
Saint-Venant-Exner model under physical boundary conditions.
