Necessary and sufficient conditions for consensus over random independent and identically distributed switching graphs

Alireza Tahbaz-Salehi*, Ali Jadbabaie

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Scopus citations

Abstract

In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discrete-time and continuous-time stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discrete-time case, our assumption is that the underlying graph of the system at any given time instance is derived from a random graph process, independent of other time instances. These graphs can be weighted, directed and with dependent edges. For the continuous-time case, we assume that the switching is governed by a Poisson point process and the graphs characterizing the topology of the system are independent and identically distributed over time. For both such frameworks, we present necessary and sufficient conditions for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. These easily verifiable conditions depend on the spectrum of the average weight matrix and the average Laplacian matrix for the discrete-time and continuous-time cases, respectively.

Original languageEnglish (US)
Title of host publicationProceedings of the 46th IEEE Conference on Decision and Control 2007, CDC
Pages4209-4214
Number of pages6
DOIs
StatePublished - Dec 1 2007
Event46th IEEE Conference on Decision and Control 2007, CDC - New Orleans, LA, United States
Duration: Dec 12 2007Dec 14 2007

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other46th IEEE Conference on Decision and Control 2007, CDC
CountryUnited States
CityNew Orleans, LA
Period12/12/0712/14/07

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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