Stability of the continuous-time Altafini model

Ji Liu, Xudong Chen, Tamer Başar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper considers the continuous-time Altafini model for opinion dynamics in which the interaction among a group of agents is described by a piecewise-constant switching signed digraph (or directed graph). Building on an idea proposed in [1], stability of the system described by the model is studied using a graphical approach. It is shown that for any sequence of repeatedly jointly strongly connected digraphs, without any assumption on the sign structure of the graphs, the system asymptotically reaches a consensus in absolute value, including convergence to zero and different types of bipartite consensus (or two-clustering). Necessary and sufficient conditions for exponential stability with respect to each possible type of limit states are provided. Specifically, under the assumption of repeatedly jointly strong connectivity, it is shown that (1) a certain type of two-clustering will be reached exponentially fast for almost all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally balanced corresponding to that type of two-clustering; (2) the system will converge to zero exponentially fast for all initial conditions if, and only if, the sequence of signed digraphs is repeatedly jointly structurally unbalanced.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1930-1935
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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  • Cite this

    Liu, J., Chen, X., & Başar, T. (2016). Stability of the continuous-time Altafini model. In 2016 American Control Conference, ACC 2016 (pp. 1930-1935). [7525201] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525201