This paper provides necessary and sufficient conditions for mean-square state-feedback stabilization of linear systems whose white noise sources have intensities affinely related to the variance of the signal they corrupt. Systems with such noise sources have been called FSN (finite signal-to-noise) models, and the stability results provided in prior work were only sufficient conditions. Upper bounded L-2 performance is also guaranteed herein by solving a control problem which is non-convex only due to a certain scaling parameter. By fixing this parameter convex programming algorithms provide controllers.