Automatic machines have recently advanced into diverse environments. A periodic state and an aperiodic state of the system usually have different physical meanings and require different control objectives in the diverse environments. To enable a new control approach based on the periodic and aperiodic states for the different control objectives, a periodic/aperiodic separation filter (PASF) that separates a state into a periodic state and an aperiodic state is proposed in this paper. Furthermore, using the PASF, the periodicjaperiodic state feedback control and the separation principle are established. (C) 2019 Elsevier Ltd. All rights reserved.