State-observer based two-dimensional robust repetitive control

This paper deals with the problem of designing a robust repetitive-control system for a class of plants with structured time-varying uncertainties. The repetitive control system is constructed using a combination of state observer and state feedback. A two-dimensional model of the system is used to precisely describe the characteristics of repetitive control, and a sufficient condition for the robust stability of the repetitive-control system is given in terms of a linear matrix inequality. The condition is then used to design the parameters of the state observer and state feedback. A numerical example demonstrates the effectiveness of the method.