Distributed Aperiodic Time-Triggered and Event-Triggered Consensus: A Scalability Viewpoint

We revisit distributed sampled-data consensus problems from a scalability point of view. Existing solutions in the literature for estimating the maximum sampling interval that preserves stability rely on the Lyapunov functional method. With this method, the overall closed-loop system (i.e. the overall network of agents) is treated as a time-delayed system. Here, a critical point is the scalability of the resulting stability conditions: in fact, the size of the LMIs to be solved depends on the size of the network. In contrast with this method, an easy-to-use and scalable method is presented, with stability conditions that are independent on the size of the network. It is shown that the proposed method can handle linear and Lipschitz nonlinear multiagent systems with both aperiodic time-triggered and event-triggered control in a unified way. Numerical examples show the efficiency of the proposed approach and the tightness of the estimated maximum sampling interval.