LMI-based design method of robust modified repetitive-control systems

An LMI-based method is presented in this paper to design a robust modified repetitive-control system for a class of strictly proper plants. Applying the periodicity and continuity of repetitive control, the system design is converted into the robust stabilization problem of a continuous-discrete 2D system. A LMI-based robust stability sufficient condition is derived by using linear matrix inequality (LMI) technique and Lyapunov stability theory. The condition is used directly to the design of the controller gains. This method has an advantage over other methods of designing robust modified repetitive-control system that it can adjust the control and learning actions individually by adjusting the parameters contained in the LMI. A numerical example is given to shown the effectiveness of the method.