Let A : D(A) → X be the generator of an analytic semigroup and B : V → [D(A * )] ′ a relatively bounded control operator. In this paper, we consider the stabilization of the system y ′ = Ay +Bu where u is the linear combination of a family (v1, . . . , vK ). Our main result shows that if (A * , B * ) satisfies a unique continuation property and if K is greater or equal to the maximum of the geometric multiplicities of the unstable modes of A, then the system is generically stabilizable with

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... ect to the family (v1, . . . , vK ). With the same functional framework, we also prove the stabilizability of a class of nonlinear systems when using feedback or dynamical controllers. We apply these results to stabilize the Navier-Stokes equations in 2D and in 3D by using boundary controls.