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

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  • Gambuzza, Lucia Valentina
  • Frasca, Mattia
  • Estrada, Ernesto

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.

Suggested Citation

  • Gambuzza, Lucia Valentina & Frasca, Mattia & Estrada, Ernesto, 2019. "Second-order consensus protocols based on transformed d-path Laplacians," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 183-194.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:183-194
    DOI: 10.1016/j.amc.2018.09.038
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