Recursive rank one perturbations for pole placement and cone reachability

The role of rank one perturbations in transforming the eigenstructure of a matrix has long been considered in the context of applications, especially in linear control systems. Two cases are examined in this paper: First, we propose a practical method to place the system eigenvalues (poles) in desir...

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Bibliographic Details
Published in:Applied mathematics and computation 2022-03, Vol.416, p.126732, Article 126732
Main Authors: Tsatsomeros, Michael J., Zhang, Faith
Format: Article
Language:English
Subjects:
Controllability
Observability
Perron-Frobenious property
Pole placement
Rank-one perturbation
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Summary:The role of rank one perturbations in transforming the eigenstructure of a matrix has long been considered in the context of applications, especially in linear control systems. Two cases are examined in this paper: First, we propose a practical method to place the system eigenvalues (poles) in desired locations via feedback control that is computed in terms of recursive rank one perturbations. Second, a choice of feedback control is proposed in order to achieve that a trajectory eventually enters the nonnegative orthant and remains therein for all time thereafter. The latter situation is achieved by imposing the strong Perron-Frobenius property and involves altering the eigenvalues, as well as left eigenvectors via rank one perturbations.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2021.126732