In this paper, we propose a synthesis method of multi-time-resolved control systems for discrete-time linear systems. In this method, on the basis of a low-rank model stemming from the Wedderburn rank reduction, we derive a redundant state-space realization of systems that enables a systematic design of a dynamical compensator stabilizing the short-time behavior of systems. Owing to the fact that the low-rank model has the same reachable and observable subspaces as the original system, we can systematically design a multiresolved control system while explicitly considering the short-time and long-time behavior of systems. The efficiency of the multiresolved control is shown through an illustrative example of frequency control of power systems.