Finite-time consensus based clock synchronization by discontinuous control

In this paper we develop a decentralized discontinuous algorithm which guarantees the finite time synchronization of a network of clocks, which are modeled as continuous-time integrators and are subject to unknown-but-bounded time-varying disturbances. The proposed synchronization algorithm is asynchronous and consists in a randomly applied local interaction rule. After a finite transient time, the proposed algorithm provides the approximated synchronization of the network by attenuating the destabilizing effect of the disturbances. Lyapunov analysis is carried out to substantiate the suggested algorithm, and simulation results are illustrated throughout the paper.