This paper considers the design of high-order modified repetitive control systems for periodic reference inputs with uncertain period-time. The objective of this work was to develop a new design method so that the closed-loop high-order modified repetitive control system is robustly stable with high control precision for periodic reference inputs with uncertain period-time. The parametrization of all stabilizing controllers containing three free parameters is proposed based on the Youla-Kucera parameterization. Moreover, to obtain the free parameters, the constraint conditions were converted into stability conditions in the form of Bilinear Matrix Inequalities that can be solved using the available software. In addition, the high control precision is guaranteed by designing the free parameters after the control characteristic of this control system. The validity and effectiveness of the proposed design method were verified by numerical examples.
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