Design of a Periodic Event-Based Repetitive Controller With Dynamic Output Feedback for Linear Systems

In this paper a periodic event-based repetitive controller with dynamic output feedback is designed for linear systems with exogenous disturbances. The periodic event mechanism is designed such that within any two event triggering instants, the dynamic output feedback controller is open which substantially reduces the control and communication burden when the output does not change significantly. First, by employing the input delay approach, the overall system consisting of the physical plant, the repetitive controller, and the dynamic output feedback controller with periodic event-triggering mechanism is modeled as a closed-loop time-varying delay system. Then, sufficient conditions in terms of linear matrix inequalities are derived to ensure that the closed-loop system is asymptotically stable with a prescribed H_∞ attenuation performance level. The controller gains are synthesized by using a matrix decomposition technique. A numerical example is provided to evaluate the proposed design approach.