Robust preview repetitive control for <scp>LPV</scp> Markovian jump system with partly unknown transition probabilities

Abstract This study addresses the preview repetitive control (PRC) issue on discrete‐time linear parameter‐varying (LPV) Markovian jump system (MJS) with partly unknown transition probabilities via linear fractional representation (LFR). To enhance periodic tracking performance, we propose a tracking controller design that integrates both repetitive control and preview actions. First, we construct an equivalent augmented model via an error system approach and the LFR framework. This model incorporates future reference signal information, thereby converting the PRC problem into a stabilization challenge. Subsequently, we develop two distinct PRC schemes to achieve tracking for the augmented system. Stability analysis and controller design leverage the Lyapunov function approach under a slack‐variable framework. Lastly, we validate the performance through two illustrative examples.