A Necessary and Sufficient Condition for Consensus Over Random Networks

Articles:

Title:: A Necessary and Sufficient Condition for Consensus Over Random Networks
Author(s):: Tahbaz-Salehi, Alireza
Jadbabaie, Ali
Date:: 2008
Type:: Articles
Department:: Business
Volume:: 53
Permanent URL:: http://hdl.handle.net/10022/AC:P:11098
Book/Journal Title:: IEEE Transactions on Automatic Control
Abstract:: We consider the consensus problem for stochastic discrete-time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability
Subject(s):: Business
Economic theory
DOI:: http://dx.doi.org/10.1109/TAC.2008.917743