In this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem (H(infinity)) as well as to the LQG (H-2) problem in periodic systems using the lifting technique. Both problems involve a causality condition on the optimal LTI compensator when viewed in the lifted domain. The H(infinity) problem is solved using Nehari’s theorem whereas in the H-2 problem the solution is obtained using the Projection theorem. Exactly the same methods of solution can be applied in the case of multirate sampled data systems. Finally, stability robustness issues in periodic and multirate systems are analyzed.