Abstract
The Laplacian controllability of a family of graphs that are non-simple is studied in the paper. Without the regular assumption that the adjacency matrix is binary, the authors consider more flexible weighting parameters to represent the practical connection strength between nodes. Suppose the node states of the graphs evolve according to the Laplacian dynamics. The Laplacian eigenspaces of a class of ring graphs are explored, by which a sufficient condition to render the graphs controllable with the minimum number of input is proposed. Numerical examples are provided to illustrate the theoretical results.
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