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In this paper, we study exact controllability and feedback stabilization for the distributed parameter control system described by high-order KdV equation posed on a periodic domain T with an internal control acting on an arbitrary small nonempty subdomain ω of T. On one hand, we show that the distributed parameter control system is locally exactly controllable with the help of Bourgain smoothing effect; on the other hand, we prove that the feedback system is locally exponentially stable with an arbitrarily large decay rate when Slemrod’s feedback input is chosen. AMS Subject Classifications: 93B05, 93D15, 35Q53 Chinese Library Classifications: O175.2, O175.4, O29

Control and Stabilization of High-Order KdV Equation Posed on the Periodic Domain