Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems (RCS) based on two-dimensional (2D) discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality (LMI) method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.