Design of periodic event-triggered control for polynomial systems: a delay system approach

Event-triggered control is a control strategy which allows the savings of communication resources in networked control systems. In this paper, we are interested in periodic event-triggering mechanisms in the sense that the triggering condition is only verified at predefined periodic sampling instants, which automatically ensures that Zeno behavior does not occur. We consider the case where both the output measurement and the control input are transmitted asynchronously using two independent triggering conditions. The developed result is dedicated to a class of nonlinear systems, where both the plant model and the feedback law can be described by polynomial functions. The overall problem is modeled and analyzed in the framework of time-delay systems, which allows to derive sum-of-squares (SOS) conditions to guarantee the global asymptotic stability in terms of the sampling period and the parameters of the triggering conditions. The approach is illustrated on a nonlinear numerical example.