Nonnegative edge consensus of networked linear systems

In this paper, nonnegative edge consensus of systems steered by general linear dynamics on directed network is investigated. In the new approach, one first endows dynamics to each directed edge and then designs a distributed edge consensus protocol guiding all edges to reach a common state. With the help of line graph theory, it is proved that strongly connected network can ensure reaching nonnegative edge consensus, if the initial conditions of all edges are nonnegative. Numerical simulations are provided to verify the theoretical results.