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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 1.
discrete time systems, graph theory, linear systems, stochastic systems, time-varying systems, average weight matrix, random graph process, random networks, stochastic discrete-time linear dynamical systems
Alireza Tahbaz-Salehi and Ali Jadbabaie, "A Necessary and Sufficient Condition for Consensus Over Random Networks", . April 2008.
Date Posted: 23 September 2009
This document has been peer reviewed.