On Zeno Behavior in Event-Triggered Finite-Time Consensus of Multiagent Systems

This article studies Zeno behavior, where an infinite number of events occur in a finite-time interval, in the event-triggered multiagent systems that aim at achieving consensus in finite time. Two popular scenarios in the first-order multiagent systems with model-based event-triggered controllers are considered. One is that the event trigger in each agent samples the absolute information, and decides when to broadcast the information to its neighbors, and the other is that the update of control signals is only scheduled by the local event triggers via directly using the (combined) relative information. The events are triggered when the measurement error between the agent, and model states violates a given threshold function. Both cases are studied, where the threshold is generated by the agent state or by the model state. Then, sufficient conditions on the existence of Zeno behavior in event-triggered finite-time consensus of multiagent systems are provided. For the triggering conditions with the thresholds given by agent states, the system must exhibit Zeno behavior; while in the case of using model states, the existence of Zeno behavior is influenced by the properties of the communication topology, and the threshold functions. Finally, several simulations, and examples are provided to illustrate the effectiveness of the theoretical results.