This paper presents a performance analysis of nonlinear periodically time-varying discrete controllers acting upon a linear time-invariant discrete plant. Time-invariant controllers are distinguished from strictly periodically time-varying controllers. For a given nonlinear periodic controller. a time-invariant controller is constructed. Necessary and sufficient conditions are given under which the time-invariant controller gives strictly better control performance than the time-invariant controller from which it was obtained, for the attenuation of l(p) exogenous disturbances and the robust stabilization of l(p) unstructured perturbations, for all p is an element of [1, infinity]. (c) 2006 Elsevier Ltd. All rights reserved.