A Multirate Approach to Event-Triggered Control of Periodic Sampled-Data Systems

In this article, we study the problem of designing event-triggering conditions for linear periodic discrete-time systems. Our design satisfies the so-called nontriviality property, a discrete-time version of the Zeno-free property, and enforces triggering events to be separated at least by two sampling periods. We propose a multirate event-based controller, in which trigger checking and control update are performed at different rates, which serves to capture the intersampling behavior. Two different architectures are proposed based on the lifting-based approach, where the original periodic system is isomorphically lifted to a higher order linear time-invariant one. Finally, the efficiency of the proposed methods is illustrated through a numerical example.