Agreement Problems in Networks with Directed Graphs and Switching Topology

In this paper, we provide tools for convergence and performance analysis of an agreement protocol for a network of integrator agents with directed information °ow. We also analyze algorithmic robustness of this consensus protocol for networks with mobile nodes and switching topology. A connection is established be-tween the Fiedler eigenvalue of the graph Laplacian and the performance of this agreement protocol. We demon-strate that a class of directed graphs, called balanced graphs, have a crucial role in solving 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 agreement protocol for networks with directed graphs and switch-ing topology.