Finite-time consensus for a network of perturbed double integrators by second-order sliding mode technique

This paper considers the problem of achieving consensus in a network of agents whose dynamics consist of perturbed double integrators. The considered class of perturbations is a bounded additive uncertainty, different for each agent, and such that the maximal magnitude is the only information available a-priori. Agents are supposed to interact through an undirected, static and connected, communication topology. The main contribution of the present work is a discontinuous local interaction rule which is able to provide finite time consensus while completely rejecting the effect of the perturbations. The local interaction rule, whose performance is investigated by Lyapunov approach, is accompanied by a set of simple tuning rules for setting the algorithm´s parameters. Simulation results demonstrate the effectiveness of the suggested scheme.