Event-based consensus control of multi-agent systems by LMI theory

This paper investigates the consensus problem of multi-agent systems by the event-based control strategy, and develops the protocol design method using the LMI (linear matrix inequality) theory. Firstly, for the closed-loop system under the event-based protocol with communication events triggered asynchronously, the norm of state disagreement vector is evaluated by giving an upper bound that is closed related to the feedback matrix of the consensus protocol. On this basis, the LMI theory is applied to determine the feedback matrix that ensures some kind of optimal consensus performance with a smaller convergence domain of disagreement vector and meanwhile a faster convergence speed. It shows that all agents will converge to a desired bounded region around the consensus trajectory under the proposed protocol.