This paper is concerned with robust state-feedback controller synthesis for discrete-time linear periodic/time-invariant systems subject to polytopic-type parametric uncertainties. In recent studies, some of the authors conceived an LMI-based approach to periodically time-varying memory controller (PTVMC) synthesis and proved that this approach is indeed effective to get less conservative robust controller design procedures. However, since the peculiar controller structure requires to reset memory to zero in a periodic way, it is pointed out that the control performance depends on the timing of implementation. In this paper we tackle this issue and propose a reset-less state-feedback Periodic FIR Controller (PFIRC), which turns out to be suitable to improve robustness on periodic and time-invariant systems. Moreover, as a special case, a design condition is provided for FIR-type LTI controllers that robustly stabilize uncertain LTI systems. Numerical examples illustrate the efficiency of the proposed approaches.