Dynamic average consensus with topology balancing under a directed graph

In this paper, the distributed average tracking problem is studied on the premise of a strongly connected directed graph. To this end, we propose a weight balance strategy that could potentially make the adjacency matrix doubly stochastic for any strongly connected directed graph. The proposed scheme is fully distributive with finite time convergence and we again prove that network connectivity (described by the first left eigenvector) is instrumental in networked control systems. Then, a discrete-time average tracking observer is introduced to ensure that all networked systems can track the average of the reference signals with bounded error. Simulation results verify the effectiveness of the proposed methods.