η(t)-consensus of multi-agent systems with directed graphs via event-triggered principles

Abstract In this paper, we investigate η ( t )-consensus problem of the multi-agent system with directed graph via event-triggered principles. The η ( t )-consensus is defined as the difference between agents’ states less than a certain preassigned time-dependent bound function η ( t ). This concept can be regarded as a generalization of the existing concepts such as quasi-consensus/synchronization, where the state differences are requested below a certain constant bound, and exponential synchronization, where the state differences converge to zero exponentially, and more generally, μ -consensus, where the state differences converge to zero with diverse convergence ratios and patterns. The event-triggering principles are asynchronous for each agent and rely on the bound function η ( t ), as well as its derivative, the agent’s own state information and some algebraic information of the network, to determine the next trigger time. We prove that with a loose assumption of the bound function, if the graph is strongly connected graph or generally possesses a spanning tree, then the proposed principles realize η ( t )-consensus of the multi-agent system, and moreover, the Zeno behavior is excluded. We give several numerical examples to illustrate the effectiveness of the theoretical results.