Vector-valued gossip over w-holonomic networks

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Authors

Publication Details

Journal
Automatica
Published
2026-09-22
DOI
https://doi.org/10.1016/j.automatica.2026.113288
Primary Topic
Opinion Dynamics and Social Influence
Type
article
Field-Weighted Citation Impact
0.00
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article

Vector-valued gossip over w-holonomic networks

Mohamed-Ali Belabbas, Tamer Başar, Erkan Bayram
Automatica
Opinion Dynamics and Social Influence
article

Vector-valued gossip over w-holonomic networks

Mohamed-Ali Belabbas, Tamer Başar, Erkan Bayram
article en

Abstract

We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "$w$-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.

AutomaticaVol. 195
Openalex Percentile: Top 100%
Opinion Dynamics and Social Influence
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