Design of equivalent-input-disturbance estimator based modified repetitive control with adaptive periodic event-triggered for time-varying delay nonlinear systems

This article addresses the problems of the disturbance rejection and the periodic signal tracking for a class of time-varying delay nonlinear systems subjected to unknown exogenous disturbances. To approximate the nonlinearity of the system, a Takagi-Sugeno (T-S) fuzzy model has been used. The proposed modified repetitive controller (MRC) scheme based on the equivalent-input-disturbance (EID) estimator improves the performance of periodic and aperiodic unknown disturbances rejection effectively and achieves good tracking performance for periodic references. Furthermore, an adaptive periodic event triggered mechanism based fuzzy state observer (APETM-FSO) has been utilized to reduce data transmission, energy consumption, and computational burden, save the resources of communication. With the help of a designed adaptive event triggering condition, the APETM can detect the event occurrence, which is described by exceeding the error signal to a predetermined threshold. Only when the event occurs, the current data are transmitted otherwise, data can be kept unchanged using a zero-order hold. Hence, The MRC, EID, and APETM-FSO based on a time-varying delay T-S fuzzy model construct the overall system. Then, to achieve the asymptotic stability of the overall system subjected to unknown disturbances, sufficient conditions based on the Lyapunov-Krasovskii functional stability theory and linear matrix inequalities (LMIs) are derived. In addition, the FSO and fuzzy state feedback controller gains are designed using the matrix decomposition and LMI approaches. Simulation results with comparative study are presented to demonstrate the effectiveness and feasibility of the proposed scheme.