A method of designing a robust modified repetitive-control system based on a continuous-discrete twodimensional(
2D) model is proposed for a class of strictly proper plants with time-varying periodic uncertainties. In the
modified repetitive-control system, the insertion of a low-pass filter makes control and learning coupled together. Employing
a continuous lifting technique, a continuous-discrete 2D model is established, where the 2D control law is in the form of direct
sum of control and learning effects. Then, the Lyapunov stability theory is used to derive a linear-matrix-inequality(LMI)
based sufficient robust stability condition. Two tuning parameters in the LMI enable the preferential adjustment of the control
and learning actions. Finally, a numerical example shows the effectiveness of the proposed method.