Equivalent-input-disturbance-based preview repetitive control for Takagi-Sugeno fuzzy systems

This paper investigates the preview repetitive control (PRC) problem for a class of Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties and external disturbances. First, a nonlinear plant is repre-sented by a T-S fuzzy model and a fuzzy equivalent-input-disturbance (EID)-based PRC law is used to im-prove the tracking performance and disturbance attenuation. Next, by using a new equality constraint, a continuous-discrete two-dimensional (2D) system is established and the design problem of the EID-based PRC law is transformed into the stability problem of such a 2D system. Then, a sufficient stability con-dition is derived in terms of linear matrix inequality (LMI). Moreover, the LMI-based parametric method for the controller is provided. Different from the existing LQR-based PRC design method, the LMI-based one can be easily achieved by the powerful Matlab's LMI Toolbox. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the developed controller design technique.(c) 2023 European Control Association. Published by Elsevier Ltd. All rights reserved.