Tight estimates for convergence of some non-stationary consensus algorithms

Details Tight estimates for convergence of some non-stationary consensus algorithms Tight estimates for convergence of some non-stationary consensus algorithms

2007-06-05

arxiv.org/abs/0706.0630v1

Mathematics

Optimization and Control

17 pages, 5 figures

Scientific paper

The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of the arcs are allowed to vary as a function of time. Under the hypothesis that some spanning tree structure is preserved along time, and that some nonzero minimal weight of the information transfer along this tree is guaranteed, an estimate of the contraction rate is given. The latter is expressed explicitly as the spectral radius of some matrix depending upon the tree depth and the lower bounds on the weights.

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