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In this paper, we examine the parametrization of all stabilizing multi-period repetitive controllers with the specified input-output frequency characteristics. The parametrization of all stabilizing multi-period repetitive controllers was considered by Yamada et al. However, when we design a stabilizing modified repetitive controller using the parametrization by Yamada et al., the inputoutput frequency characteristics of the control system cannot be settled so easily. From the practical point of view, the input-output frequency characteristics of the control systems are required to be easily settled. This problem is solved by obtaining the parametrization of all stabilizing multi-period repetitive controllers with the specified input-output frequency characteristics. In this paper, we expand the result by Yamada et al. and propose the parametrization of all stabilizing multi-period repetitive controllers with the specified input-output frequency characteristics. The roles of freeparameters in the parametrization are also clarified. Then it is shown that the input-output frequency characteristic and the disturbance attenuation characteristics can be settled independently.

The Parametrization of All Stabilizing Multi-period Repetitive Controllers with the Specified Input-output Frequency Characteristics