Almost Decouplability of any Directed Weighted Network Topology

This paper introduces a conception that any weighted directed network topology is almost decouplable, which can help to transform the topology into a similar form being composed of uncoupled vertices, and thus reduce the complexity of analysis for networked dynamical systems. As an example of its application, the consensus problem of linear multi-agent systems with time-varying network topologies is addressed. As a result, a necessary and sufficient condition for uniform consensus is proposed.