A Simple Proof of the Continuous Time Linear Consensus Problem with Applications in Non-Linear Flocking Networks

We revisit the linear distributed consensus problem in continuous time, to provide a simple and elegant proof under very mild assumptions. Our approach is based on a novel extension of the contraction coefficient that can be adapted to the continuous time version of the model. We apply our results in non-linear second order consensus networks of Cucker-Smale type and we obtain new initial conditions for asymptotic flocking.