Paper Info
Title
Convergence Results for the Linear Consensus Problem under Markovian Random Graphs.
Abstract
This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.
Year
DOI
Venue
2013
10.1137/100816870
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
consensus,Markovian random graphs,stochastic systems
Graph theory,Consensus,Discrete mathematics,Indifference graph,Mathematical optimization,Markov process,Random graph,Matrix (mathematics),Discrete time and continuous time,Strongly connected component,Mathematics
Journal
Volume
Issue
ISSN
51
2
0363-0129
Citations 
PageRank 
References 
32
1.13
9
Authors
3
Name
Order
Citations
PageRank
Ion Matei114913.66
John S. Baras21953257.50
Christoforos Somarakis35512.13