Second-order consensus protocols based on transformed d-path Laplacians

Lucia Valentina Gambuzza, Mattia Frasca and Ernesto Estrada

Applied Mathematics and Computation, 2019, vol. 343, issue C, 183-194

Abstract: The Laplacian of a graph mathematically formalizes the interactions occurring between nodes/agents connected by a link. Its extension to account for the indirect peer influence through longer paths, weighted as a function of their length, is represented by the notion of transformed d-path Laplacians. In this paper, we propose a second-order consensus protocol based on these matrices and derive criteria for the stability of the error dynamics, which also consider the presence of a communication delay. We show that the new consensus protocol is stable in a wider region of the control gains, but admits a smaller maximum delay than the protocol based on the classical Laplacian. We show numerical examples to illustrate our theoretical results.

Keywords: Consensus,; d-path Laplacians; Communication delay (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:183-194

DOI: 10.1016/j.amc.2018.09.038

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