  In this paper, we solve the problem of exponential stabilization for a class
of cascade ODE-PDE system governed by a linear ordinary differential equation
and a 1-d linearized Korteweg-de Vries equation (KdV) posed on a bounded
interval. The control for the entire system acts on the left boundary with
Dirichlet condition of the KdV equation whereas the KdV acts in the linear ODE
by a Dirichlet connection. We use the socalled backstepping design in infinite
dimension to convert the system under consideration into an exponentially
stable cascade ODE-PDE system.Then, we use the invertibility of such design to
achieve the exponential stability for the ODE-PDE cascade system under
consideration by using Lyapunov analysis.
