Design of Robust Discrete-Time Observer-Based Repetitive-Control System

This paper concerns the design of a robust discrete-time observer-based repetitive-control system for a class of linear plants with periodic uncertainties. A discrete two-dimensional model is built that partially uncouples the control and learning actions of a repetitive-control system, enabling their preferential adjustment. The combination of a singular-value decomposition of the output matrix and Lyapunov stability theory is used to derive a linear-matrix-inequality-based design algorithm that determines the control and state-observer gains. A numerical example illustrates the main advantage of the method: easy, preferential adjustment of control and learning by means of two tuning parameters in an linear-matrix-inequality-based condition.