Observer-based H∞ fuzzy control for modified repetitive control systems

In this paper, the periodic tracking control problem is considered for nonlinear systems with some parameters uncertainties and disturbances. First, a T-S fuzzy approach is employed to model nonlinear systems. Second, considering the partly state unmeasured and periodic tracking reference signal, fuzzy state observer and fuzzy modified repetitive controller (FMRCr) are designed based on the modified repetitive control (MRC) approach. To achieve signal tracking and H∞ disturbance attenuation performance, a two-dimensional model approach and singular-value decomposition technique of system output matrix are developed. Then, by the Lyapunov stability theory, some sufficient conditions are obtained for FMRC closed-loop system with stabilization and H∞ disturbance attenuation performance in linear matrix inequality (LMI) form. Correspondingly, the controller gains and observer gains are solved by LMI toolbox. Two numerical examples are provided to illustrate the validity of the method.