Design of observer-based robust repetitive-control system

Repetitive control, a distinctive control method with a human-like learning capability, is of both theoretical and practical importance. This paper deals with the problem of designing a robust observer-based repetitive-control system that provides a given H_¿ steady-state disturbance-attenuation performance for a class of plants with time-varying structured uncertainties. A continuous-discrete two-dimensional hybrid model is built that accurately describes the features of repetitive control so as to enable independent adjustment of the control and learning actions. A sufficient condition for the repetitive-control system to have a steady-state disturbance-attenuation bound in the H_¿ setting is given in terms of a linear matrix inequality. The condition is then used to obtain the parameters of the repetitive controller and the state observer. Finally, a numerical example demonstrates the effectiveness of the method.