Design of a modified repetitive control system using state feedback based on two-dimensional hybrid model

This paper presents a method of designing a modified repetitive control system (MRCS) based on a two-dimensional (2D) continuous-discrete hybrid model. First, a 2D continuous-discrete hybrid model of MRCS is established. Next, the design of the feedback controller of the MRCS is converted to the stabilization problem of the 2D hybrid system with a static-state feedback. Then, by using a 2D Lyapunov method, a sufficient stability condition for the 2D hybrid system is derived in terms of a linear matrix inequality. Furthermore, the result is extended to handle a plant with a time-varying uncertainty. These conditions can be used to obtain the parameters of a feedback controller and a low-pass filter in the MRCS. The validity of the method is demonstrated by numerical examples.