This note presents a periodic compensator which achieves robust stability for single-input-single-output (SISO), linear time invariant (LTI) plants having both right-half plane (RRP) poles and zeros, a job LTI controllers fail to do. In addition, for strictly proper plants this controller achieves model matching ensuring at the same time that the periodic oscillations present in the plant output are insignificant in magnitude. The design steps are straightforward and linear algebraic in nature.