Finite-time consensus in directed switching network topologies and time-delayed communications

There are many practical situations where it is desirable or even required to achieve stable convergence in the finite-time domain. In this paper, a simple distributed continuous-time protocol is introduced that guarantees finite-time consensus in networks of autonomous agents. Protocol convergence in weighted directed/undirected and fixed/switching networks is explored based on a Lyapunov analysis. The stability of the system and the solvability of the consensus algorithm are proved for network topologies that contain a spanning tree frequently enough over contiguous time intervals. The decision value for different topologies and for multi-rate integrator agents is investigated, and a novel approach is proposed to determine the leader subgroup of agents. Communication time-delay and chattering phenomenon in the system are assessed, and additionally some protocols with Lipschitz right-hand sides are introduced. Herein, all proposed consensus strategies use a limited-gain control input to account for the physical limitation of control actuation devices, which, in general, are subject to amplitude saturation.