Weighted average-consensus for directed networks of multi-agent with switching topology

The consensus problem in directed networks of multiagent is studied. A new notion, called weighted average-consensus, is proposed and a class of distributed controller is applied to achieve global asymptotically weighted average-consensus in networks of multiagent with fixed and switching topology. We establish a connection between the Fiedler eigenvalue of the graph Laplacian and the performance of this consensus controller. It is proved theoretically that the strongly connectedness of directed graph and a class of directed graphs, called balanced graphs, play a crucial role in solving weighted average-consensus problems. Based on the properties of balanced graphs, a group disagreement function (i.e. Lyapunov function) is proposed for convergence analysis of this consensus controller in directed networks and for robustness analysis in directed networks with switching topology. Finally, simulation example is provided for consensus problem in networks with switching topology to validate the theoretical results.