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arXiv · 1303.6674

Consensus Algorithms and the Decomposition-Separation Theorem

Sadegh Bolouki·Roland P. Malhame
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Abstract

Convergence properties of time inhomogeneous Markov chain based discrete and continuous time linear consensus algorithms are analyzed. Provided that a so-called infinite jet flow property is satisfied by the underlying chains, necessary conditions for both consensus and multiple consensus are established. A recenet extension by Sonin of the classical Kolmogorov-Doeblin decomposition-separation for homogeneous Markov chains to the inhomogeneous case is then employed to show that the obtained necessary conditions are also sufficient when the chain is of Class P*, as defined by Touri and Nedic. It is also shown that Sonin's theorem leads to a rediscovery and generalization of most of the existing related consensus results in the literature.

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Sadegh Bolouki, Roland P. Malhame. 2013-03-26. Consensus Algorithms and the Decomposition-Separation Theorem. https://arxiv.org/abs/1303.6674

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