Products of generalized stochastic Sarymsakov matrices
2016 (English)In: Proceedings of the IEEE Conference on Decision and Control, IEEE conference proceedings, 2016, 3621-3626 p.Conference paper (Refereed)Text
In the set of stochastic, indecomposable, aperiodic (SIA) matrices, the class of stochastic Sarymsakov matrices is the largest known subset (i) that is closed under matrix multiplication and (ii) the infinitely long left-product of the elements from a compact subset converges to a rank-one matrix. In this paper, we show that a larger subset with these two properties can be derived by generalizing the standard definition for Sarymsakov matrices. The generalization is achieved either by introducing an SIA index, whose value is one for Sarymsakov matrices, and then looking at those stochastic matrices with larger SIA indices, or by considering matrices that are not even SIA. Besides constructing a larger set, we give sufficient conditions for generalized Sarymsakov matrices so that their products converge to rank-one matrices. The new insight gained through studying generalized Sarymsakov matrices and their products has led to a new understanding of the existing results on consensus algorithms and will be helpful for the design of network coordination algorithms.
Place, publisher, year, edition, pages
IEEE conference proceedings, 2016. 3621-3626 p.
Algebra and Logic
IdentifiersURN: urn:nbn:se:kth:diva-188261DOI: 10.1109/CDC.2015.7402780ScopusID: 2-s2.0-84962003979ISBN: 9781479978861OAI: oai:DiVA.org:kth-188261DiVA: diva2:937429
54th IEEE Conference on Decision and Control, CDC 2015, 15 December 2015 through 18 December 2015
QC 201606152016-06-152016-06-092016-06-15Bibliographically approved