Group Consensus of Linear Multi-agent Systems under Nonnegative Directed Graphs

Zhongchang Liu, Wing Shing Wong

Group consensus implies reaching multiple convergence groups where agents belonging to the same cluster converge. This paper focuses on linear multi-agent systems under nonnegative directed graphs. A new necessary and sufficient condition for ensuring group consensus is derived, which requires the spanning forest of the underlying directed graph and that of its quotient graph induced with respect to a clustering partition to contain equal minimum number of directed trees. This condition is further shown to be equivalent to containing cluster spanning trees, a commonly used topology for the underlying graph in the literature. Under a designed controller gain, lower bound of the overall coupling strength for achieving group consensus is specified. Moreover, the pattern of the multiple synchronous states formed by all clusters is characterized by setting the overall coupling strength be large enough.

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