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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2022-08-01
|
| Series: | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/124028/PDF/BPASTS_2022_70_6_3132.pdf |
| _version_ | 1797954392100438016 |
|---|---|
| author | Tadeusz Kaczorek |
| author_facet | Tadeusz Kaczorek |
| author_sort | Tadeusz Kaczorek |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T23:16:53Z |
| format | Article |
| id | doaj.art-ae00353100b94fa4b4bc0dff9e6543e0 |
| institution | Directory Open Access Journal |
| issn | 2300-1917 |
| language | English |
| last_indexed | 2024-04-10T23:16:53Z |
| publishDate | 2022-08-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Bulletin of the Polish Academy of Sciences: Technical Sciences |
| spelling | doaj.art-ae00353100b94fa4b4bc0dff9e6543e02023-01-12T18:21:27ZengPolish Academy of SciencesBulletin of the Polish Academy of Sciences: Technical Sciences2300-19172022-08-01706https://doi.org/10.24425/bpasts.2022.141987Eigenvalues assignment in uncontrollable linear systemsTadeusz Kaczorek0https://orcid.org/0000-0002-1270-3948Białystok University of Technology, ul. Wiejska 45A, 15-351 Białystok, PolandIt 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.https://journals.pan.pl/Content/124028/PDF/BPASTS_2022_70_6_3132.pdfcontrollabilityeigenvaluesassignmentlinear systemfeedbackprocedure component |
| spellingShingle | Tadeusz Kaczorek Eigenvalues assignment in uncontrollable linear systems Bulletin of the Polish Academy of Sciences: Technical Sciences controllability eigenvalues assignment linear system feedback procedure component |
| title | Eigenvalues assignment in uncontrollable linear systems |
| title_full | Eigenvalues assignment in uncontrollable linear systems |
| title_fullStr | Eigenvalues assignment in uncontrollable linear systems |
| title_full_unstemmed | Eigenvalues assignment in uncontrollable linear systems |
| title_short | Eigenvalues assignment in uncontrollable linear systems |
| title_sort | eigenvalues assignment in uncontrollable linear systems |
| topic | controllability eigenvalues assignment linear system feedback procedure component |
| url | https://journals.pan.pl/Content/124028/PDF/BPASTS_2022_70_6_3132.pdf |
| work_keys_str_mv | AT tadeuszkaczorek eigenvaluesassignmentinuncontrollablelinearsystems |