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A Necessary and Sufficient Condition for Consensus Over Random Networks

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2 Author(s)
Tahbaz-Salehi, A. ; Univ. of Pennsylvania, Philadelphia ; Jadbabaie, A.

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.

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Automatic Control, IEEE Transactions on  (Volume:53 ,  Issue: 3 )