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Node‐to‐node bipartite consensus of multi‐agent systems with disturbances

This study presents a novel concept of consensus for multi-agent systems with a two-layer framework, namely, the node-to-node bipartite consensus. The agents are divided into the virtual leaders and followers, and the signed graph representing communication channels of followers is supposed to be structurally balanced. Moreover, only a small part of the followers are pinned by their corresponding leaders. In addition, the proposed control is subjected to Gaussian disturbances or norm-bounded disturbances, and two extended forms of node-to-node bipartite consensus are correspondingly defined. By utilising the signed graph theory, the M-matrix theory, and the Lyapunov function approach, the consensus error between an arbitrary follower and its leader is proved to converge to zero in the mean square sense or to be ultimately bounded. The proposed conditions for consensus mainly depend on the selection of pinned followers and the coupling strength in each layer. Finally, the theoretical results are illustrated by detailed numerical examples.