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Consensus Over Ergodic Stationary Graph Processes
Open accessAbstract
In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process. We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate.
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Cites
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Jadbabaie, A., Lin, J., & Morse, A. S. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.812781 · Cited by 8,339
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Acemoglu, D., Ozdaglar, A., & ParandehGheibi, A. (2010) · Games and Economic Behavior · doi:10.1016/j.geb.2010.01.005 · Cited by 444
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Metadata
- Authors
- Tahbaz-Salehi, A., & Jadbabaie, A.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2010-01
- Volume
- 55
- Issue
- 1
- Pages
- 225-230
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- OpenAlex
- W2160413708
- Cited by
- 233
- References
- 2
- FWCI
- 27.44
- Type
- journal article
- Language
- en
- Open access
- green
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