@ARTICLE{Kaczorek_Tadeusz_Eigenvalues_2022,
author={Kaczorek, Tadeusz},
volume={70},
number={6},
pages={e141987},
journal={Bulletin of the Polish Academy of Sciences Technical Sciences},
howpublished={online},
year={2022},
abstract={It is shown that in uncontrollable linear system ẋ = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.},
title={Eigenvalues assignment in uncontrollable linear systems},
type={Article},
URL={http://www.czasopisma.pan.pl/Content/124028/PDF-MASTER/BPASTS_2022_70_6_3132.pdf},
keywords={controllability, eigenvalues, assignment, linear system, feedback, procedure component},
}