The parameterization of all robust stabilizing simple repetitive controllers for multiple-input/multiple-output plants

The simple repetitive control system proposed by Yamada et al. is a type of servomechanism for the periodic reference input. That is, the simple 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 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 repetitive controllers. Recently, the parameterization of all robust stabilizing simple repetitive controllers for the plant with uncertainty was clarified by Yamada et al. However, they did not clarify the parameterization of all robust stabilizing simple repetitive controllers for multipleinput/multiple-output plants. Since many real plants include uncertainty and have multipleinput and multiple-output, this is the important problem to solve. The purpose of this paper is to propose the parameterization of all robust stabilizing simple repetitive controllers for multiple-input/multiple-output plants.