On Conditions for Convergence to Consensus

Author

Lorenz, Jan ; Lorenz, Dirk A.

Author_Institution

Dept. of Syst. Design, ETH Zurich, Zurich, Switzerland

Volume

55

Issue

7

fYear

2010

fDate

7/1/2010 12:00:00 AM

Firstpage

1651

Lastpage

1656

Abstract

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 [6] (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.

Keywords

Lyapunov methods; convergence; discrete time systems; multi-agent systems; time-varying systems; topology; Lyapunov theory; Moreau theorem; averaging map; consensus; convergence; discrete dynamical system; multiagent system; switching communication topology; time-dependent system; Asymptotic stability; Communication switching; Convergence; Distributed computing; Multiagent systems; Protocols; State-space methods; System analysis and design; Tin; Topology; Unmanned aerial vehicles; Averaging map; consensus protocol; multiagent systems; set-valued Lyapunov theory;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2046086

Filename

5437323