A class of event-triggered coordination algorithms for multi-agent systems on weight-balanced digraphs

This paper revisits the multi-agent average consensus problem on weight-balanced directed graphs. In order to reduce communication among the agents, many recent works have considered event-triggered communication and control as a method to reduce communication while still ensuring that the entire network converges to the desired state. One common way to do this is to design events such that a specifically chosen Lyapunov function is monotonically decreasing; however, depending on the chosen Lyapunov function the transient behaviors can be very different. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting network and exclusion of Zeno behavior. This allows us to easily consider the implementation of different algorithms that all guarantee correctness to be able to meet varying performance needs. Simulations are provided to illustrate our findings.