Mason, Oliver and Wirth, Fabian (2014) Extremal norms for positive linear inclusions. Linear Algebra and its Applications, 444. pp. 100-113. ISSN 0024-3795

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Abstract

For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to absolute norms. The semigroups under consideration may be generated by discrete-time systems, continuous-time systems or continuous-time systems with jumps. The existence of extremal norms is used to extend results on the Lipschitz continuity of the joint spectral radius beyond the known case of semigroups that are irreducible in the representation theory interpretation of the word.

Item Type:	Article
Additional Information:	This is the preprint version of the published article, which is available at doi:10.1016/j.laa.2013.11.020
Keywords:	Joint spectral radius; extremal norm; linear switched systems; linear semigroups;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute Faculty of Science and Engineering > Mathematics and Statistics
Item ID:	6228
Identification Number:	https://doi.org/10.1016/j.laa.2013.11.020
Depositing User:	Oliver Mason
Date Deposited:	02 Jul 2015 14:54
Journal or Publication Title:	Linear Algebra and its Applications
Publisher:	Elsevier
Refereed:	Yes
URI:	http://www.sciencedirect.com/science/jou...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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