  In this paper we present an abstract maximal $L^p$-regularity result up to $T
= \infty$, that is tuned to capture (linear) Partial Differential Equations of
parabolic type, defined on a bounded domain and subject to finite dimensional,
stabilizing, feedback controls acting on (a portion of) the boundary.
Illustrations include, beside a more classical boundary parabolic example, two
more recent settings: (i) the $3d$-Navier-Stokes equations with finite
dimensional, localized, boundary tangential feedback stabilizing controls as
well as Boussinesq systems with finite dimensional, localized, feedback,
stabilizing, Dirichlet boundary control for the thermal equation.
