Abstract
Barabanov norms have been introduced in Barabanov (Autom. Remote Control, 49 (1988), pp. 152--157) and constitute an important instrument in analyzing the joint spectral radius of a family of matrices and related issues. However, although they have been studied extensively, even in very simple cases it is very difficult to construct them explicitly (see, e.g., Kozyakin (Discrete Contin. Dyn. Syst. Ser. B, 14 (2010), pp. 143--158)). In this paper we give a canonical procedure to construct them exactly, which associates a polytope extremal norm---constructed by using the methodologies described in Guglielmi, Wirth, and Zennaro (SIAM J. Matrix Anal. Appl., 27 (2005), pp. 721--743) and Guglielmi and Protasov (Found. Comput. Math., 13 (2013), pp. 37--97)---to a polytope Barabanov norm. Hence, the existence of a polytope Barabanov norm has the same genericity of an extremal polytope norm. Moreover, we extend the result to polytope antinorms, which have been recently introduced to compute the lower spectral radi...
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
