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Stabilization of Parabolic Nonlinear Systems with Finite Dimensional Feedback or Dynamical Controllers: Application to the Navier–Stokes System
Let $A:\mathcal{D}(A)\to\mathcal{X}$ be the generator of an analytic semigroup and $B:\mathcal{V}\to[\mathcal{D}(A^*)]'$ 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 $(v_1,\ldots,v_K)$. Our main result shows that if $(A^*,B^*)$ satisfies a unique continuation property and …