Design of robust repetitive control system with a state observer

The problem of designing a robust repetitive-control system is studied based on a state observer for a class of plants with structural time-varying uncertainties. The reconstructed states from the state observer are employed in the state-feedback controller design. Based on the stability theory of two-dimensional (2D) systems, a sufficient condition for the existence of the state observer and the repetitive controller for the repetitive control system are presented in terms of a linear matrix inequality (LMI) whose feasible solutions are utilized to determine the parameters of the state observer and the repetitive controller. A numerical example demonstrates the effectiveness of the method.