Eigenvalues assignment in uncontrollable linear systems
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 t...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2022-08-01
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| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
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| Online Access: | https://journals.pan.pl/Content/124028/PDF/BPASTS_2022_70_6_3132.pdf |
| Summary: | 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. |
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| ISSN: | 2300-1917 |