In this paper, we propose a new method to obtain the optimal cost ( the in mum of the achievable H(infinity) norm of a closed-loop system) for discrete linear periodically time-varying (LPTV) systems. This method reduces via the lifting technique the original problem to the H(infinity) problems of linear time-invariant (LTI) systems without the causality constraint, and therefore the optimal cost can be easily calculated. It is one of the primary advantages over other existing methods. We also show, by applying our method to LTI systems, that the optimal cost for the H(infinity) problem of discrete LTI systems cannot be improved even if we use a class of noncausal controllers. An intriguing implication of this fact is further shown in the context of causal controllers.