Second-Order Multiagent Systems with Event-Driven Consensus Control

and Applied Analysis 3 defined as f(e(t), x(t), V(t)) = 0, where x(t), V(t) ∈ Rn are, respectively, the concatenation vector of the state variables in system (3). All agents update their consensus controls u i (t) at a series of event-times τ(s) (s = 0, 1, . . .) which are implicitly defined by f(e(τ(s)), x(τ(s)), V(τ(s))) = 0. Between control updates at two consecutive event-times, the eventdriven consensus control is held constant until the next event is triggered, that is, u i (t) = u i (τ (s)) , ∀t ∈ [τ (s) , τ (s + 1)) . (5) We say that the event-driven consensus problem of leaderless multi-agent system (3) is solved if an event-driven consensus control can be found to ensure that lim t→∞ 󵄨󵄨󵄨󵄨 x i (t) − x j (t) 󵄨󵄨󵄨󵄨 = 0, lim t→∞ 󵄨󵄨󵄨󵄨 V i (t) − V j (t) 󵄨󵄨󵄨󵄨 = 0, (6) for i, j ∈ V. Similarly, the event-driven consensus problem of leader-follower multi-agent system (3)-(4) is solved if lim t→∞ 󵄨󵄨󵄨󵄨xi (t) − x0 (t) 󵄨󵄨󵄨󵄨 = 0, lim t→∞ 󵄨󵄨󵄨󵄨Vi (t) − V0 (t) 󵄨󵄨󵄨󵄨 = 0, (7)