Some Categorical Properties of Linear Systems
Linear control systems are studied by means of a state-space approach. Feedback morphisms are presented as natural generalization of feedback equivalences. The set of feedback morphisms between two linear systems is a vector space. Kernels, cokernels, as well as monomorphisms, epimorphisms, sections...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/2088 |
| _version_ | 1797484680889499648 |
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| author | Miguel V. Carriegos |
| author_facet | Miguel V. Carriegos |
| author_sort | Miguel V. Carriegos |
| collection | DOAJ |
| description | Linear control systems are studied by means of a state-space approach. Feedback morphisms are presented as natural generalization of feedback equivalences. The set of feedback morphisms between two linear systems is a vector space. Kernels, cokernels, as well as monomorphisms, epimorphisms, sections, and retracts of feedback morphisms are studied in the category of linear systems over finite dimensional vector spaces. Finally, a classical Kalman’s decomposition of linear systems over vector spaces is presented as a split short exact sequence in the category. |
| first_indexed | 2024-03-09T23:07:54Z |
| format | Article |
| id | doaj.art-7769c170e4b740cf9b21aab74e85e0b5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:07:54Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7769c170e4b740cf9b21aab74e85e0b52023-11-23T17:49:32ZengMDPI AGMathematics2227-73902022-06-011012208810.3390/math10122088Some Categorical Properties of Linear SystemsMiguel V. Carriegos0Departamento of Matemáticas, Universidad de León, 24071 León, SpainLinear control systems are studied by means of a state-space approach. Feedback morphisms are presented as natural generalization of feedback equivalences. The set of feedback morphisms between two linear systems is a vector space. Kernels, cokernels, as well as monomorphisms, epimorphisms, sections, and retracts of feedback morphisms are studied in the category of linear systems over finite dimensional vector spaces. Finally, a classical Kalman’s decomposition of linear systems over vector spaces is presented as a split short exact sequence in the category.https://www.mdpi.com/2227-7390/10/12/2088feedbacklinear systemscategorical properties of feedback actions |
| spellingShingle | Miguel V. Carriegos Some Categorical Properties of Linear Systems Mathematics feedback linear systems categorical properties of feedback actions |
| title | Some Categorical Properties of Linear Systems |
| title_full | Some Categorical Properties of Linear Systems |
| title_fullStr | Some Categorical Properties of Linear Systems |
| title_full_unstemmed | Some Categorical Properties of Linear Systems |
| title_short | Some Categorical Properties of Linear Systems |
| title_sort | some categorical properties of linear systems |
| topic | feedback linear systems categorical properties of feedback actions |
| url | https://www.mdpi.com/2227-7390/10/12/2088 |
| work_keys_str_mv | AT miguelvcarriegos somecategoricalpropertiesoflinearsystems |