Summary: Let A be the generator of a \(C_ 0\) semigroup T(t), \(t\geq 0\), and denote by S(t), \(t\geq 0\), the semigroup generated by A-K, where K is a bounded linear operator on a Hilbert space. In this note we find necessary and sufficient conditions for the original semigroup T(t), \(t\geq 0\), to be exponentially stable, given that the ''feedback'' semigroup S(t), \(t\geq 0\), is exponentially stable. Applications to feedback stabilization via a steady-state Riccati equation will then be made.