Design of Observer-Based $H_{\infty }$ Robust Repetitive-Control System

This technical note deals with the problem of designing a robust observer-based repetitive-control system that provides a given H_∞ disturbance attenuation performance for a class of plants with time-varying structured uncertainties. A continuous-discrete two-dimensional model is built that accurately describes the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A sufficient condition for the repetitive-control system to have a disturbance-attenuation bound in the H_∞ setting is given in terms of a linear matrix inequality (LMI). It yields the parameters of the repetitive controller and the state observer. Finally, a numerical example demonstrates the effectiveness of the method, whose main advantage is the easy, preferential adjustment of control and learning through the tuning of two parameters in the LMI-based condition.