Recursive rank one perturbations for pole placement and cone reachability

Michael J. Tsatsomeros and Faith Zhang

Applied Mathematics and Computation, 2022, vol. 416, issue C

Abstract: 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.

Keywords: Rank-one perturbation; Controllability; Observability; Pole placement; Perron-Frobenious property (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008146

DOI: 10.1016/j.amc.2021.126732

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