Finite-Time Consensus Using Stochastic Matrices With Positive Diagonals

Author

Hendrickx, Julien M. ; Guodong Shi ; Johansson, Karl H.

Author_Institution

ICTEAM Inst., Univ. Catholique de Louvain, Louvain la Neuve, Belgium

Volume

60

Issue

4

fYear

2015

fDate

Apr-15

Firstpage

1070

Lastpage

1073

Abstract

We discuss the possibility of reaching consensus in finite time using only linear iterations, with the additional restrictions that the update matrices must be stochastic with positive diagonals and consistent with a given graph structure. We show that finite-time average consensus can always be achieved for connected undirected graphs. For directed graphs, we show some necessary conditions for finite-time consensus, including strong connectivity and the presence of a simple cycle of even length.

Keywords

directed graphs; graph theory; matrix algebra; mobile robots; stochastic processes; connected undirected graphs; directed graphs; finite-time average consensus; graph structure; linear iterations; matrix update; necessary conditions; positive diagonals; strong connectivity; Autonomous agents; Conferences; Convergence; Educational institutions; Indexes; Optimization; Signal processing algorithms; Agents and autonomous systems; finite-time consensus; sensor networks;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2352691

Filename

6887337