On the existence of common Lyapunov functions for consensus algorithms based on averaging

Authors

MEHMET AKAR
ROBERT SHORTEN

Abstract

This paper addresses distributed deterministic consensus algorithms based on averaging. We relate the conditions for achieving consensus to the existence of a common norm for a set of row-stochastic matrices associated with the original set of averaging matrices. For a system to achieve consensus, it is shown that this associated set of matrices should have a Common Lyapunov Function, even if the original set might not have one.

DOI

10.3906/elk-1002-23

Keywords

Consensus, synchronization, scrambling matrix, common Lyapunov function, switched systems

First Page

483

Last Page

493

Recommended Citation

AKAR, MEHMET and SHORTEN, ROBERT (2011) "On the existence of common Lyapunov functions for consensus algorithms based on averaging," Turkish Journal of Electrical Engineering and Computer Sciences: Vol. 19: No. 3, Article 12. https://doi.org/10.3906/elk-1002-23
Available at: https://journals.tubitak.gov.tr/elektrik/vol19/iss3/12