Finite-Time Consensus with Disturbance Rejection by Discontinuous Local Interactions in Directed Graphs

In this technical note we propose a decentralized discontinuous interaction rule which allows to achieve consensus in a network of agents modeled by continuous-time first-order integrator dynamics affected by bounded disturbances. The topology of the network is described by a directed graph. The proposed discontinuous interaction rule is capable of rejecting the effects of the disturbances and achieving consensus after a finite transient time. An upper bound to the convergence time is explicitly derived in the technical note. Simulation results, referring to a network of coupled Kuramoto-like oscillators, are illustrated to corroborate the theoretical analysis.