Event-triggered consensus control for a class of two-time-scale multi-agent systems

The consensus control problem is studied for a class of two-time-scale multi-agent systems with the event-triggered mechanism (ETM). Under the communication topology, an event-based control scheme is proposed for each agent by utilising the relative measurement information between the agent itself and its neighbouring ones. A sampled-data-based ETM is constructed to decide when the current data-packet should be broadcast. This scheme takes full advantage of relative error-based ETM, and thus leading to a high efficiency of data transmissions. By virtue a novel singular perturbation parameter-dependent Lyapunov-Krasovskii functional, stability criteria and sufficient conditions for the consensus control algorithm and ETM are derived to guarantee that the state error dynamics is asymptotically stable. Furthermore, by using the proposed consensus controller design method, the ill-conditioned numerical issues caused by the two-time-scale property can also be avoided, and the upper bound of singular perturbation parameter is deduced explicitly. Finally, two convincing examples are employed to demonstrate the validity and effectiveness of the proposed transmission scheme and consensus control protocol.