Mean square stability of consensus over fading networks with nonhomogeneous communication delays

Jing Wang, Nicola Elia

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

9 Scopus citations

Abstract

In this paper, we propose a discrete time consensus protocol which can solve the consensus problem in the network with nonhomogeneous communication delays. We give the sufficient conditions to reach consensus and provide a closed form formula for the consensus value. Furthermore, we investigate the mean square stability (MSS) of our protocol when each link of the network can break with a given probability at each time interval. The condition for checking MSS is equivalent to checking the spectral radius of a positive matrix. To gain more insight, we further restrict our attention to spatially invariant network structure and develop a more efficient expression to check the MSS. We derive a closed form formula to determine the MSS in the limit of large delays, get useful lower and upper bounds and analyze their implications for large classes of network topologies. We find that the consensus protocol is robust to link failures in the sense the system is always mean square stable if we put restrictions on the propagation gain.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
Pages4614-4619
Number of pages6
DOIs
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other47th IEEE Conference on Decision and Control, CDC 2008
CountryMexico
CityCancun
Period12/9/0812/11/08

Keywords

  • Mean-square stability robustness
  • Network consensus
  • Spatially invariant systems

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  • Cite this

    Wang, J., & Elia, N. (2008). Mean square stability of consensus over fading networks with nonhomogeneous communication delays. In Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008 (pp. 4614-4619). [4739345] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2008.4739345