Let us consider a fluid-rigid body interaction system. We are interested in the feedback stabilization of this system by using a finite-dimensional control localized on the interface between the structure and the fluid. The fluid is assumed to be viscous and incompressible and to follow the Navier-Stokes system and we consider for the rigid body the Newton laws. We follow a general method for the stabilization of nonlinear parabolic systems combined with a change of variables to handle the fact that the fluid domain is moving with time. We prove that for small initial velocities and if the initial position and the final position are close, we can stabilize the position and the velocity of the rigid body and the velocity of the fluid.
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