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Abstract

It is shown that in uncontrollable linear system = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜnm if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix  M ∈ ℜnm 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.

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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID

  1. Białystok University of Technology, ul. Wiejska 45A, 15-351 Białystok, Poland

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