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A Necessary and Sufficient Condition for Consensus Over Random Networks
Abstract
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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Cites
Consensus Problems in Networks of Agents With Switching Topology and Time-Delays
Olfati-Saber, R., & Murray, R. M. (2004) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2004.834113 · Cited by 12,788
Coordination of groups of mobile autonomous agents using nearest neighbor rules
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Self-citationNonnegative Matrices in the Mathematical Sciences
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PROBABILITY: THEORY AND EXAMPLES
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A scheme for robust distributed sensor fusion based on average consensus
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Cited by
On Distributed Convex Optimization Under Inequality and Equality Constraints
Zhu, M., & Martinez, S. (2012) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2011.2167817 · Cited by 759
Opinion Dynamics and Learning in Social Networks
Acemoglu, D., & Ozdaglar, A. (2011) · Dynamic Games and Applications · doi:10.1007/s13235-010-0004-1 · Cited by 705
A tutorial on modeling and analysis of dynamic social networks. Part I
Proskurnikov, A. V., & Tempo, R. (2017) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2017.03.002 · Cited by 553
Group consensus in multi-agent systems with switching topologies and communication delays
Yu, J., & Wang, L. (2010) · Systems & Control Letters · doi:10.1016/j.sysconle.2010.03.009 · Cited by 485
Cao, Y., Ren, W., & Meng, Z. (2010) · Systems & Control Letters · doi:10.1016/j.sysconle.2010.06.002 · Cited by 405
Metadata
- Authors
- Tahbaz-Salehi, A., & Jadbabaie, A.
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2008-04
- Volume
- 53
- Issue
- 3
- Pages
- 791-795
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- 2334-3303
- OpenAlex
- W2114403255
- Cited by
- 431
- References
- 20
- FWCI
- 63.10
- Type
- journal article
- Language
- en
- Open access
- closed
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