Two-Channel Periodic Event-Triggered Observer-Based Repetitive Control for Periodic Reference Tracking

This paper proposes a two-channel periodic event-triggered observed-based repetitive control strategy to track a periodic reference signal subject to limited communication capacity. Under the designed two-channel periodic event-triggering framework, within any two consecutive event-triggering instants in each event-triggering channel, not only the output measurements to the state observer but also the observer states to the repetitive controller structure are kept unchanged via a zero-order hold (ZOH) which can substantially alleviate the communication burden when the output measurements and the observer states do not change significantly. By employing the input delay approach, the overall system consisting of the physical plant, the state observer, the repetitive controller, and the two-channel periodic event-triggering mechanisms is modeled as a closed-loop time-varying delay system. Sufficient conditions in terms of linear matrix inequalities are derived to ensure the closed-loop system to be asymptotically stable with a prescribed $H$∞attenuation performance level for an exogenous disturbance input. The controller gains, observer gains, and the event-triggering parameters are synthesized by using a matrix decomposition technique. A numerical example is provided to evaluate the proposed design approach.