The use of finite-dimensional linear time-invariant controllers for the stabilization of periodic solutions in sinusoidally forced nonlinear systems is investigated. By mixing results concerning absolute stability of nonlinear systems and robustness of linear systems, a linear matrix inequality-based controller synthesis technique is developed. The synthesis algorithm yields the controller maximizing a lower bound of the maximum amplitude of the forcing input, for which the corresponding periodic solutions are guaranteed to be stable. The Duffing oscillator is employed to illustrate the main features of the proposed synthesis technique.