Reference : Consensus in non-commutative spaces
Scientific congresses and symposiums : Paper published in a book
Engineering, computing & technology : Electrical & electronics engineering
http://hdl.handle.net/2268/82667
Consensus in non-commutative spaces
English
Sepulchre, Rodolphe mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Sarlette, Alain mailto [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation >]
Rouchon, Pierre [Mines ParisTech > Centre Automatique et Systemes > > Professor >]
Dec-2010
Proceedings of the 49th IEEE Conference on Decision and Control
IEEE
6596-6601
Yes
Atlanta
GA
49th IEEE Conference on Decision and Control
from 15-12-2010 to 17-12-2010
IEEE
Atlanta
GA
[en] Hilbert metric ; positive definite cone ; Kraus maps
[en] 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.
Systems and Modeling
Fonds de la Recherche Scientifique (Communauté française de Belgique) - F.R.S.-FNRS ; Pole d'attraction interuniversitaire DYSCO
Researchers ; Students ; General public
http://hdl.handle.net/2268/82667

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