Two Consensus problems of Homogenous Multi-Agent Systems with Directed Topology: A Unified Viewpoint

This paper considers both the leader-following and leaderless consensus problems of homogenous multi-agent systems with directed topologies. Different from the existing results, in which these two consensus problems are investigated separately using different approaches, M-matrix theory based approach in the leader-following case and the eigenvalues based approach in the leaderless case, by introducing some related properties of the graph Laplacian matrix, a unified analysis framework for these two consensus problems is first proposed. This fills the gap between these two consensus problems. It is shown that the leaderless case can include the leader-following case as a special case. Not only analytical consensus value but also the disagreement values are also clearly induced here. Since the proposed properties of the graph Laplacian matrix are independent of the graph being symmetric or not, it allows us to overcome the difficulties induced by the asymmetry of the directed topology for analysis. Moreover, the conclusions are obtained with general dynamics and topology conditions, then the analysis framework for consensus problem introduced here can be seen as a fundamental tool to deal with other consensus problems.

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