On Conditions for Convergence to Consensus

Details On Conditions for Convergence to Consensus On Conditions for Convergence to Consensus

2008-03-14

arxiv.org/abs/0803.2211v2

Mathematics

Optimization and Control

5 pages, 2 columns, example added

Scientific paper

10.1109/TAC.2010.2046086

A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005) about set-valued Lyapunov theory and convergence under switching communication topologies. We give examples that point out differences of approaches including examples where Moreau's theorem is not applicable but ours is. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.

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