Convergence rate of the modified DeGroot-Friedkin model with doubly stochastic relative interaction matrices

Weiguo Xia, Ji Liu, Karl H. Johansson, Tamer Başar

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

Abstract

In a recent paper [1], a modified DeGroot-Friedkin model was proposed to study the evolution of the social-confidence levels of individuals in a reflected appraisal mechanism in which a network of n individuals consecutively discuss a sequence of issues. The individuals update their self-confidence levels on one issue in finite time steps, via communicating with their neighbors, instead of waiting until the discussion on the previous issue reaches a consensus, while the neighbor relationships are described by a static relative interaction matrix. This paper studies the same modified DeGroot-Friedkin model, but with time-varying interactions which are characterized by a sequence of doubly stochastic matrices. It is shown that, under appropriate assumptions, the n individuals' self-confidence levels will all converge to 1/n exponentially fast. An explicit expression of the convergence rate is provided.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1054-1059
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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