Event-triggered Formation Control of Multi-agent Systems with Time Delay via Complex-valued Laplacian

Formation problem of first-order multi-agent systems is considered via complex-valued Laplacian. The event-triggered controller with time delay is designed for each agent. Formation can reach specific but arbitrary formation shape for some time delays under the assumption that the interconnection graph of the multi-agent systems is 2-rooted. Furthermore, the Zeno-behavior is excluded for the closed-loop system. Finally, a simulation example is given to illustrate the efficiency of the proposed results.