Preview Repetitive Control for Linear Discrete-Time Systems

This paper addresses the preview repetitive control (PRC) for discrete-time systems for a given previewed reference signal. Firstly, an augmented error system (AES) is constructed. Then, two kinds of PRC laws are proposed, and a two-dimensional (2D) model is presented. Using Lyapunov functions, sufficient conditions for asymptotic stability of the 2D system are derived and the designs of PRC laws are proposed via the LMI method. Finally, the effectiveness of our proposed PRC is illustrated by a numerical simulation examples.