Robust Preview Repetitive Control of T-S Fuzzy Markovian Jump Systems via Partially Uncertain Transitions

Abstract

This work presents a novel methodology for preview repetitive control (PRC) in nonlinear Markovian jump systems (MJS) with partially unknown transition probabilities, utilizing Takagi-Sugeno (T-S) fuzzy modeling. The study addresses the challenge by constructing an augmented error model (AEM) for T-S fuzzy MJS in the presence of time-varying uncertainties, thereby transforming the original fuzzy PRC problem into a stability analysis task for the AEM. Two distinct fuzzy PRC schemes are then developed based on the system's state and output information of the T-S fuzzy MJS, incorporating previewed reference signals for enhanced performance. Sufficient stability conditions for the AEM and controller design criteria are rigorously derived through Lyapunov stability theory combined with linear matrix inequality (LMI) techniques. The effectiveness of the proposed control strategies is validated through two illustrative simulation examples, demonstrating their practical applicability and performance advantages.