Finite-time Consensus for Third-Order Multi-Agent Systems with Directed Communication Networks

This paper focuses on third-order multi-agent systems with directed communication networks. It is for the first time that the finite-time consensus problem is solved for third-order multi-agent systems under digraphs containing spanning trees. Two explicit-coefficient finite-time protocols, namely, edge-based and node-based, are proposed. First, we prove that asymptotic consensus is achievable with the reduced linear protocol. Then, we show that finite-time consensus is achievable with our explicit-coefficient finite-time protocols through homogeneous theory. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed protocols.