Modified repetitive periodic event-triggered control with equivalent-input-disturbance for linear systems subject to unknown disturbance

This paper studies the disturbance rejection and the periodic signal tracking problems for linear systems with unknown exogenous disturbances under limited communication resources. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC). Furthermore, a periodic event-triggered feedback observer (PETFO) is proposed to reduce the computational burden and energy consumption, and saving communication resources. The PETFO observes the occurrence of a predetermined event or not, where the current data are transmitted only when the event occurs otherwise, there is a zero-order hold keeps the data unchanged. The stability of the overall systems is guaranteed using the Lyapunov Krasovskii functional theory and linear matrix inequalities (LMIs). The observer and the controller gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme.