Almost Decouplability of any Directed Weighted Network Topology

TL;DR

This paper proposes that any weighted directed network can be approximately decoupled into simpler components, facilitating analysis of complex networked systems, with applications demonstrated in multi-agent consensus problems.

Contribution

It introduces the concept of almost decouplability for directed networks and applies it to derive a necessary and sufficient condition for consensus.

Findings

Any directed weighted network is almost decouplable.

Derived a necessary and sufficient condition for uniform consensus.

Simplified analysis of networked dynamical systems.

Abstract

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.