A new method for the design of fixed-order Linear Parameter Varying (LPV) controllers with polytopic representation for LTI plants is proposed. The stability constraints for the closed-loop system are presented through a set of Linear Matrix Inequalities (LMIs). An additional set of LMIs guarantees H1 performance for the weighted closed-loop sensitivity function. The method is successfully applied to the problem of controller design for the rejection of a sinusoidal disturbance with time-varying frequency.