A necessary and sufficient condition for consensus over random networks

Alireza Tahbaz-Salehi*, Ali Jadbabaie

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

325 Scopus citations

Abstract

We consider the consensus problem for stochastic discrete-time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1.

Original languageEnglish (US)
Pages (from-to)791-795
Number of pages5
JournalIEEE Transactions on Automatic Control
Volume53
Issue number3
DOIs
StatePublished - Apr 2008

Keywords

  • Consensus problem
  • Random graphs
  • Tail events
  • Weak ergodicity

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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