Average consensus in the presence of delays in directed graph topologies

Christoforos N. Hadjicostis, Themistoklis Charalambous

Research output: Contribution to journalArticleScientificpeer-review

83 Citations (Scopus)


Classical distributed algorithms for asymptotic average consensus typically assume timely and reliable exchange of information between neighboring components of a given multi-component system. These assumptions are not necessarily valid in practice due to varying delays that might affect computations at different nodes and/or transmissions at different links. In this work, we propose a protocol that overcomes this limitation and, unlike existing consensus protocols in the presence of delays, ensures asymptotic consensus to the exact average, despite the presence of arbitrary (but bounded) delays in the communication links. The protocol requires that each component has knowledge of the number of its out-neighbors (i.e., the number of components to which it can send information) and its proof of correctness relies on the weak convergence of a backward product of column stochastic matrices. The proposed algorithm is demonstrated via illustrative examples.

Original languageEnglish
Article number6571230
Pages (from-to)763-768
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed


  • Average consensus
  • bounded delays
  • digraphs
  • ratio consensus
  • weak convergence

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