A note on the eigenvectors of perturbed matrices with applications to linear positive systems
Linear Algebra and Its Applications
© 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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.
The present research was supported by EPSRC grant EP/I019456/1.
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.
Vol. 509, pp. 143 - 167