Explicit computation of sampling period in periodic event-triggered multi-agent control

This paper investigates the synchronization of nonlinear sampled-data multi-agent systems. The purpose is to obtain an explicit formula for the maximum allowable sampling period (MASP) that guarantees exponential synchronization. Two implementation scenarios are considered. We first propose an approach on finding the MASP for periodic time-triggered sampled-data control. Then, a periodic event-triggered communication and control strategy is formulated, where a communication function and a control function are designed for each agent to determine whether or not the sampled data or the control input should be transmitted at each sampling instant. It is shown that there is a tradeoff between the sampling frequency and the convergence performance. The theoretical results are illustrated in simulations.