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

Christopher Guiver, Dave Hodgson, Stuart Townley

Research output: Contribution to journalArticle

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 may
help estimate or control transient dynamics. The results apply to both discrete- and continuous-time linear positive systems. The theory is illustrated with several examples.
LanguageEnglish
Pages143-167
JournalLinear Algebra and its Applications
Volume509
DOIs
StatusPublished - 15 Nov 2016

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Positive Systems
Eigenvalues and eigenfunctions
Eigenvector
Linear Systems
Structured Perturbations
Irreducible Matrix
Transient Dynamics
Lyapunov functions
Lyapunov Function
Continuous Time
Non-negative
Norm
Estimate
Class

Cite this

A note on the eigenvectors of perturbed matrices with applications to linear positive systems. / Guiver, Christopher; Hodgson, Dave; Townley, Stuart.

In: Linear Algebra and its Applications, Vol. 509, 15.11.2016, p. 143-167.

Research output: Contribution to journalArticle

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