Distributed Consensus of Linear Multi-Agent Systems with Switching Directed Topologies

TL;DR

This paper develops conditions for achieving distributed consensus in linear multi-agent systems with switching directed topologies by transforming the problem into a stabilization issue and applying stability analysis techniques.

Contribution

It introduces a novel approach converting the consensus problem into a stabilization problem for switched linear systems, providing new sufficient conditions for consensus.

Findings

Consensus is achievable if each agent is stabilizable.

Presence of a directed spanning tree in each topology is sufficient.

Numerical simulation validates the theoretical results.

Abstract

This paper addresses the distributed consensus problem for a linear multi-agent system with switching directed communication topologies. By appropriately introducing a linear transformation, the consensus problem is equivalently converted to a stabilization problem for a class of switched linear systems. Some sufficient consensus conditions are then derived by using tools from the matrix theory and stability analysis of switched systems. It is proved that consensus in such a multi-agent system can be ensured if each agent is stabilizable and each possible directed topology contains a directed spanning tree. Finally, a numerical simulation is given for illustration.