This note considers a stabilization problem for a class of uncertain linear systems containing structured uncertainty described by a certain Integral Quadratic Constraint. Tile notion of stabilizability considered is that of absolute stabilizability. The main result gives a necessary and sufficient condition for the absolute stabilizability of this class of uncertain systems in terms of tile existence of a solution to a corresponding "diagonally scaled" H-infinity control problem. It follows from this result that absolute stabilizability via nonlinear control implies absolute stabilizability via linear control.