Search for: [Abstract = "In order to describe the interconnection among agents with multi\-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights \(or weighted interconnection coefficients\) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi\-dimensional interconnections, while using nonnegative definite matrices to denote partial multi\-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi\-dimensional integrators."]

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