Periodic event-triggered formation control of multi-agent systems via complex Laplacian

The event-triggered formation control of first-order continuous multi-agent systems is studied based on complex Laplacian in this paper. Periodic event-triggered control is designed in which continuous communication between agents is not required. For each agent, two different triggering conditions are discussed. The first one relies on the inter-neighboring communication at each verification time, while the second one only need the broadcast states of neighbors at their triggering instants. According to the Lyapunov stability theory and algebraic graph theory, consensus conditions on the verification period and parameters in the triggering conditions are also provided. It is demonstrated that the maximum verification period under two triggering conditions are two times larger than the existing results. And a certain amount of communication between neighbors can be further reduced in the second one. Finally, the simulation examples prove the validity of the results proposed.