Periodic event-triggered consensus based on triggered communication states for multi-agent systems with packet losses

In this paper, periodic event-triggered leaderless and leader-following consensus problems are studied for linear multi-agent systems with deterministic packet losses under the generic directed communication topology. Specially, an event-triggered mechanism is proposed, which only needs to communicate the event-triggered states of the agent and verify the event-triggered condition at the periodic sampling instants. A switched system with stable and unstable subsystems is used to describe packet dropouts in a deterministic way. The incidence matrix of a directed spanning tree in the directed communication topology is utilized to construct a linear transformation so that the consensus problems are equivalently transformed into the asymptotic stability problems of reduced-order systems. Then, some sufficient consensus conditions are derived and the consensus protocol gains are designed. Finally, simulation examples are given to show the effectiveness of the proposed results.