### 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.

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 |
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Pages (from-to) | 143-167 |

Journal | Linear Algebra and its Applications |

Volume | 509 |

DOIs | |

Publication status | Published - 15 Nov 2016 |

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### Cite this

Guiver, C., Hodgson, D., & Townley, S. (2016). A note on the eigenvectors of perturbed matrices with applications to linear positive systems.

*Linear Algebra and its Applications*,*509*, 143-167. https://doi.org/10.1016/j.laa.2016.07.010