This paper deals with feedback stabilization of second order equations of
the form
ytt + A0y + u (t) B0y (t) = 0, t ∈ [0, +∞[,
where A0 is a densely defined positive selfadjoint linear operator on a
real Hilbert space H, with compact inverse and B0 is a linear map in diagonal form. It is
proved here that the classical sufficient ad-condition of Jurdjevic-Quinn and
Ball-Slemrod with the feedback control u = ⟨yt, B0y⟩H implies the
strong stabilization. This result is derived from a general compactness
theorem for semigroup with compact resolvent and solves several open problems.