CUED Publications database

Consensus in non-commutative spaces

Sepulchre, R and Sarlette, A and Rouchon, P (2010) Consensus in non-commutative spaces. In: UNSPECIFIED pp. 6596-6601..

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Convergence analysis of consensus algorithms is revisited in the light of the Hilbert distance. The Lyapunov function used in the early analysis by Tsitsiklis is shown to be the Hilbert distance to consensus in log coordinates. Birkhoff theorem, which proves contraction of the Hilbert metric for any positive homogeneous monotone map, provides an early yet general convergence result for consensus algorithms. Because Birkhoff theorem holds in arbitrary cones, we extend consensus algorithms to the cone of positive definite matrices. The proposed generalization finds applications in the convergence analysis of quantum stochastic maps, which are a generalization of stochastic maps to non-commutative probability spaces. ©2010 IEEE.

Item Type: Conference or Workshop Item (UNSPECIFIED)
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:15
Last Modified: 09 Sep 2021 01:34
DOI: 10.1109/CDC.2010.5717072