Finite-Time Consensus for High-Order Multiagent Systems Under Directed Communication Topologies

This article addresses the finite-time consensus problem for multiagent systems with directed information exchange graphs under the spanning tree assumption. A crucial strategy is to develop a homogeneous approach that goes beyond existing Lyapunov-based methods for finite-time consensus of multiagent systems subject to undirected information exchange graphs and accordingly symmetric Laplacian matrices. This article proposes two classes of distributed controllers (edge-based and node-based) for multiagent systems modeled by chains of integrators without assuming symmetric information exchange graphs.The finite-time consensus analysis is carried out by constructing a novel Lyapunov function based on the homogeneous theory. Interestingly, the proposed method can also be extended to multiagent systems with linear or nonlinear dynamics under specific conditions.