Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees
- 1 January 2009
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 48 (1), 1-32
- https://doi.org/10.1137/060673527
Abstract
International audienceResults for estimating the convergence rate of nonstationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries). The results appear to be tight in a number of instances and are illustrated through simple as well as more sophisticated examples. The main idea is to follow propagation of information along certain spanning-trees which arise in the communication graphKeywords
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This publication has 18 references indexed in Scilit:
- Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays, and Asynchronous EventsSIAM Journal on Control and Optimization, 2008
- Stability of leaderless discrete-time multi-agent systemsMathematics of Control, Signals, and Systems, 2006
- On the second eigenvalue of matrices associated with TCPLinear Algebra and its Applications, 2006
- Randomized gossip algorithmsIEEE Transactions on Information Theory, 2006
- Estimating the Second Largest Eigenvalue of a Markov Transition MatrixBernoulli, 2000
- Distributed memoryless point convergence algorithm for mobile robots with limited visibilityIEEE Transactions on Robotics and Automation, 1999
- Feedback control in coupled map latticesPhysical Review E, 1998
- On the second real eigenvalue of nonegative and Z-matricesLinear Algebra and its Applications, 1997
- Geometric Bounds for Eigenvalues of Markov ChainsThe Annals of Applied Probability, 1991
- Products of stochastic matrices and applicationsInternational Journal of Mathematics and Mathematical Sciences, 1989