Departmental Papers (ESE)

Document Type

Journal Article

Date of this Version

April 2008

Comments

Copyright 2008 IEEE. Reprinted from IEEE Transactions on Automatic Control, Volume 53, Issue 3, April 2008, pages 791-795.

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Abstract

We consider the consensus problem for stochastic discrete time linear dynamical systems. The underlying graph of such systems at a given time instance is derived from a random graph process, independent of other time instances. For such a framework, we present a necessary and sufficient condition for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. This easily verifiable condition uses the spectrum of the average weight matrix. Finally, we investigate a special case for which the linear dynamical system converges to a fixed vector with probability 1.

Keywords

consensus problem, random graphs, tail events, weak ergodicity

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Date Posted: 08 May 2008

This document has been peer reviewed.