Distributed average consensus based on structural weight-balanceability

This study presents the concept of structural weight-balanceability of network systems as a useful method to examine the average consensus of the systems. The authors introduce the notion of structurally unobservable node based on structural observability concept to determine the structural weight-balanceability of a network. They propose a simple technique to identify structurally unobservable nodes, and consequently infer on structural weight-balanceability of the network. A mathematical method based on principal minors of the associated Laplacian matrix of the network is developed to modify a structurally weight-balanceable network into a weight-balanced one. A distributed method is presented to compute normalised principal minors in a large-scale network system with directed communication topology. This is the first work that provides a rigorous mathematical formulation to check the structural weight-balanceability of network systems and make a structurally weight-balanceable network, weight-balanced. Finally, simulation results are presented to illustrate the performance of the proposed method in dealing with networks with a large number of nodes.