A note on the eigenvectors of perturbed matrices with applications to linear positive systems

Guiver, Chris; Hodgson, Dave; Townley, Stuart

Abstract

A result is presented describing the eigenvectors of a perturbed matrix, for a class of structured perturbations. One motivation for doing so is that positive eigenvectors of nonnegative, irreducible matrices are known to induce norms — acting much like Lyapunov functions — for linear positive systems, which mayhelp estimate or control transient dynamics. The results apply to both discrete- and continuous-time linear positive systems. The theory is illustrated with several examples.

• Journal Article Type: Article
• Acceptance Date: Jul 12, 2016
• Online Publication Date: Jul 16, 2016
• Publication Date: Nov 15, 2016
• Deposit Date: Jul 23, 2020
• Publicly Available Date: Aug 5, 2020
• Journal: Linear Algebra and its Applications
• Print ISSN: 0024-3795
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 509
• Pages: 143-167
• DOI: https://doi.org/10.1016/j.laa.2016.07.010
• Public URL: http://researchrepository.napier.ac.uk/Output/2677314