Control and stabilization of the periodic fifth order Korteweg-de Vries equation

We establish local exact control and local exponential stability of periodic solutions of fifth order Korteweg-de Vries type equations in H-s(& x1d54b;), s > 2. A dissipative term is incorporated into the control which, along with a propagation of regularity property, yields a smoothing effect permitting the application of the contraction principle.