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We consider a fluid-structure interaction system composed by athree-dimensional viscous incompressible fluid and an elastic plate located onthe upper part of the fluid boundary. The fluid motion is governed by theNavier-Stokes system whereas the structure displacement satisfies the dampedplate equation. We consider here the Navier slip boundary conditions. The mainresult of this work is the feedback stabilization of the strong solutions ofthe corresponding system around a stationary state for any exponential decayrate by means of a time delayed control localized on the fixed fluid boundary.The strategy here is based on the Fattorini-Hautus criterion. Then, the maintool in this work is to show the unique continuation property of the associatesolution to the adjoint system.

Local boundary feedback stabilization of a fuid-structure interaction problem under Navier slip boundary conditions with time delay