A design method for robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants

The simple multi-period repetitive control system proposed by Yamada and Takenaga is a type of servomechanism for the periodic reference input. That is, the simple multi-period repetitive control system follows the periodic reference input with small steady state error, even if a periodic disturbance or uncertainty exists in the plant. In addition, simple multi-period repetitive control systems make transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. Yamada et al. clarified the parameterization of all stabilizing simple multi-period repetitive controllers. Recently, the parameterization of all robust stabilizing simple multi-period repetitive controllers for the plant with uncertainty was clarified by Yamada et al. However, their method cannot be applied to multiple-input/multiple-output plants. In this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers for multiple-input/multiple-output plants.