摘要 :
Using the intrinsic relationship between the external equitable partition (EEP) and the spectral properties
of the graph Laplacian, we characterize convergence and observability properties of consensus dynamics on
networks. In par...
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Using the intrinsic relationship between the external equitable partition (EEP) and the spectral properties
of the graph Laplacian, we characterize convergence and observability properties of consensus dynamics on
networks. In particular, we establish the relationship between the original consensus dynamics and the associated
consensus of the quotient graph under varied initial conditions, and characterize the asymptotic convergence
to the synchronization manifold under nonuniform input signals. We also show that the EEP with respect to a
node can reveal nodes in the graph with an increased rate of asymptotic convergence to the consensus value, as
characterized by the second smallest eigenvalue of the quotient Laplacian. Finally, we show that the quotient
graph preserves the observability properties of the full graph and how the inheritance by the quotient graph
of particular aspects of the eigenstructure of the full Laplacian underpins the observability and convergence
properties of the system.
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