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Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms
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Morris, Ian D. (2010) Criteria for the stability of the finiteness property and for the uniqueness of Barabanov norms. Linear Algebra and Its Applications, Vol.433 (No.7). pp. 1301-1311. doi:10.1016/j.laa.2010.05.007 ISSN 0024-3795.
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Official URL: http://dx.doi.org/10.1016/j.laa.2010.05.007
Abstract
A set of matrices is said to have the finiteness property if the maximal rate of exponential growth of long products of matrices drawn from that set is realised by a periodic product. The extent to which the finiteness property is prevalent among finite sets of matrices is the subject of ongoing research. In this article, we give a condition on a finite irreducible set of matrices which guarantees that the finiteness property holds not only for that set. but also for all sufficiently nearby sets of equal cardinality. We also prove a theorem giving conditions under which the Barabanov norm associated to a finite irreducible set of matrices is unique up to multiplication by a scalar, and show that in certain cases these conditions are also persistent under small perturbations. (C) 2010 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Linear Algebra and Its Applications | ||||
| Publisher: | Elsevier Inc | ||||
| ISSN: | 0024-3795 | ||||
| Official Date: | 1 December 2010 | ||||
| Dates: |
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| Volume: | Vol.433 | ||||
| Number: | No.7 | ||||
| Number of Pages: | 11 | ||||
| Page Range: | pp. 1301-1311 | ||||
| DOI: | 10.1016/j.laa.2010.05.007 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | EP/E020801/01 (EPSRC) |
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