Observer‐based preview repetitive control for uncertain discrete‐time systems
Li Li
Abstract
Abstract In this paper, the preview repetitive control (PRC) problem is considered for uncertain discrete‐time systems subject to a previewable periodic reference signal. First, an augmented system including future information on the previewable reference signal is constructed. Second, considering the state unmeasured and periodic tracking reference signal, state observer and preview repetitive controller (PRCr) are designed in both state feedback and output feedback settings. To achieve signal tracking performance, a two‐dimensional (2D) model approach and some LMI technique are presented to describe the control and learning actions of the PRC system by using the lifting technique. Then, by Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of LMIs, and meanwhile, the design of a repetitive controller with preview actions is proposed through the LMI approach. Finally, two examples illustrate the effectiveness of the results.