This paper is concerned with the robust performance for linear parameter varying (LPV) discrete-time periodic systems. The time-varying parameters are supposed to belong in a compact set described by a polytope. In this way one can consider arbitrarily fast rates of variation as well as bounded rates of variation for the time-varying parameters. The H_∞ performance will be used to evaluate the LPV discrete-time periodic systems. Both primal and dual representation of the periodic system will be considered and conditions in the form of Linear Matrix Inequalities will be presented to compute the H_∞ performance. Numerical experiments will be used to illustrate the H_∞ performance computed for the primal and dual representations by applying the proposed technique in different scenarios.