The parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic

In this paper, we examine the parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. The parameterization of all stabilizing multi-period repetitive controllers, those are used to improve the disturbance attenuation characteristics of the repetitive controller, for non-minimum phase systems was solved by Yamada et al. However, when we design a stabilizing multi-period repetitive controller using the parameterization by Yamada et al., the input-output frequency characteristic of the control system cannot be settled so easily, because 2(N +1) numbers of free parameters in the parameterization related to the input-output characteristic. This problem is solved by obtaining the parameterization of all stabilizing multi-period repetitive controllers with the specified input-output frequency characteristic, which is the parameterization when the input-output characteristic is settled beforehand. From this view point, the parameterization of all stabilizing multi-period repetitive controllers with the specified input-output frequency characteristic was proposed. However, the previous result did not clarify the parameterization of all stabilizing multi-period repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. This work extends the previous results into the multiple-input/multiple-output plants.