The parameterization of all robust stabilizing simple multi-period repetitive controllers with the specified input-output characteristic

In this paper, we propose the parameterization of all robust stabilizing simple multi-period repetitive controllers with the specified input-output characteristic. Recently, Yamada et al. proposed the parameterization of all robust stabilizing simple multi-period repetitive controllers for the plant with uncertainty such that the controller works as a robust stabilizing multi-period repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have finite numbers of poles. However, using the method by Yamada et al., it is complex to specify the low-pass filters in the internal model for the periodic reference input of which the role is to specify the input-output characteristic. Because, the lowpass filters are related to three kinds of free parameters in the parameterization proposed by Yamada et al. Our proposed parameterization in this paper overcome this problem by specifying the low-pass filters in the internal model for the periodic reference input beforehand. That is, using our parameterization, we can design a robust stabilizing simple multi-period repetitive control system which has desirable input-output characteristic more easily than the method proposed by Yamada et al.