This article addresses the robust model predictive control (MPC) for systems with polytopic uncertaintydescription. In the case of multiple state delays, some results are given in the previous works. However, previousworks are not well established for input-delay systems. This article proposes new approaches that can effectivelyhandle not only the input-delay, but also the multiple delayed input. For the time-delay system, a general MPCsolution is based on the use of augmented delay-free state-space description, which can be computationallyexpensive. Hence, in general there are simplified formulations based on the time-delay description, which can beapplied in different situations. This article proposes three simplified formulations, with the first incorporating aprevious result as a special case, the second being a solution for a unique class of systems and the third being amore general solution without special assumptions on the plant. Numerical examples illustrate the effectivenessof the proposed approaches.