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

Christopher Guiver; Dave Hodgson; Stuart Townley

doi:10.1016/j.laa.2016.07.010

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

Christopher Guiver, Dave Hodgson, Stuart Townley

University of Exeter

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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.

Original language	English
Pages (from-to)	143-167
Journal	Linear Algebra and its Applications
Volume	509
DOIs	https://doi.org/10.1016/j.laa.2016.07.010
Publication status	Published - 15 Nov 2016

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10.1016/j.laa.2016.07.010

2016_06_24_eigenvector_perturbationsAccepted author manuscript, 478 KBLicence: Unspecified

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title = "A note on the eigenvectors of perturbed matrices with applications to linear positive systems",

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.",

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AU - Hodgson, Dave

AU - Townley, Stuart

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N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/84980384702

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DO - 10.1016/j.laa.2016.07.010

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VL - 509

SP - 143

EP - 167

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

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

Abstract

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