Design of a robust output-feedback-based modified repetitive-control system

This paper concerns the problem of designing a robust output-feedback-based modified repetitive-control system for a class of strictly proper plants with periodic uncertainties. Exploiting the periodicity of repetitive control, a continuous-discrete two-dimensional (2D) model is built so that the control and learning actions can be adjusted preferentially by means of the control gains. The combination of the singular-value decomposition of the output matrix and the Lyapunov stability theory is used to derive a linear-matrix-inequality-(LMI-) based asymptotic stability condition. Two tuning parameters in the LMI regulate the choice of the parameters in the 2D control law and thereby enable the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the validity of the method.