This paper presents a preview repetitive control for linear continuous-time systems when a periodic reference signal is previewed. First, an augmented two-dimensional (2D) system is constructed by state augmentation technique and a 2D model approach. Then, the preview repetitive control laws are proposed for the augmented 2D system, which transforms the preview repetitive control problem into a stabilization problem. Using Lyapunov functions, sufficient conditions for asymptotic stability of the 2D continuous-discrete system are derived in the form of linear matrix inequalities (LMIs). The design of a preview repetitive controller is proposed through the LMI approach. Finally, the developed design techniques are applied to two examples. The simulation results demonstrate the validity of the proposed method.
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