A Necessary and Sufficient Condition for Consensus Over Random Networks

Tahbaz-Salehi, Alireza; Jadbabaie, Ali

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



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IEEE Transactions on Automatic Control

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September 7, 2011