Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees

David Angeli (1) , Pierre-Alexandre Bliman (2)

1 DSI - Dipartimento di Sistemi e Informatica
2 SISYPHE - SIgnals and SYstems in PHysiology & Engineering

Results 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 graph.

Mots clés: graph theory; distributed consensus; multiagent systems; convergence rate; graph theory.

David Angeli, Pierre-Alexandre Bliman. Convergence Speed of Unsteady Distributed Consensus: Decay Estimate Along the Settling Spanning-Trees. SIAM Journal on Control and Optimization, 2009, 48 (1), pp.1-32. ⟨10.1137/060673527⟩. ⟨hal-00793004⟩