The Parametrization of All Stabilizing Multi-Period Repetitive Controllers for Time-Delay Systems with The Specified Input-Output Frequency Characteristics

In this paper, we examine the parametrization of all stabilizing multi-period repetitive controllers for single-input/single-output time-delay systems with the specified input-output frequency characteristics. The multi-period repetitive controller is proposed by Gotou et al. to improve the disturbance attenuation characteristics of the modified repetitive controllers. The parametrization of all multi-period repetitive controller for non-minimum phase systems and that of all multi-period repetitive controllers for time-delay systems were solved by Yamada and Satoh. However, using the method by Yamada and Satoh, we cannot settle input-output characteristics easily. If the parametrization of all stabilizing multi-period repetitive controllers with the specified input-output characteristics is obtained, we can specify input-output characteristics easily. In this paper, we propose the parametrization of all stabilizing multi-period repetitive controllers with the specified input-output characteristics for time-delay systems