A Necessary and Sufficient Condition for Consensus Over Random Networks

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General Robotics, Automation, Sensing and Perception Laboratory
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GRASP
consensus problem
random graphs
tail events
weak ergodicity
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Tahbaz-Salehi, Alireza
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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.

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2008-04-01
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Copyright 2008 IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 53, Issue 3, April 2008, pages 791-795. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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