Weight allocation in Laplacian matrix of random networks based on geodesic distances

Ya Zhang, Xuxin Zhang and Kecheng Liu

International Journal of Systems Science, 2020, vol. 51, issue 7, 1266-1279

Abstract: This paper proposes a novel approach to the weight allocation in the leader-following Laplacian matrix of time-invariant/random networks by using the geodesic distances. The weight of each follower node is designed as a function of an adjusting parameter in power form, and the power number is set as the geodesic distance from this node to the leader in the topology. Under the given design, lower bounds of the second smallest real part of the eigenvalues of the Laplacian matrix and the mean Laplacian matrix are explicitly provided for time-invariant and random lossy networks, respectively. The lower bounds are further applied to distributively design consensus controllers and consensus estimator, and sufficient conditions of the adjusting parameter in the weights are distributively obtained to characterise the convergence of consensus protocols. Numerical examples are given to illustrate the results.

Date: 2020
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DOI: 10.1080/00207721.2020.1758234

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