On backward product of stochastic matrices

Behrouz Touri, Angelia Nedić

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

We study the ergodicity of backward product of stochastic and doubly stochastic matrices by introducing the concept of absolute infinite flow property. We show that this property is necessary for ergodicity of any chain of stochastic matrices, by defining and exploring the properties of a rotational transformation for a stochastic chain. Then, we establish that the absolute infinite flow property is equivalent to ergodicity for doubly stochastic chains. Furthermore, we develop a rate of convergence result for ergodic doubly stochastic chains. We also investigate the limiting behavior of a doubly stochastic chain and show that the product of doubly stochastic matrices is convergent up to a permutation sequence. Finally, we apply the results to provide a necessary and sufficient condition for the absolute asymptotic stability of a discrete linear inclusion driven by doubly stochastic matrices.

Original languageEnglish (US)
Pages (from-to)1477-1488
Number of pages12
JournalAutomatica
Volume48
Issue number8
DOIs
StatePublished - Aug 2012

Keywords

  • Absolute infinite flow property
  • Averaging control
  • Discrete inclusion systems
  • Distributed control
  • Doubly stochastic matrices
  • Ergodicity
  • Product of stochastic matrices
  • Switching control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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