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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Bibliographic Details
Published in:Mathematics (Basel) 2022-06, Vol.10 (12), p.2088
Main Author: Carriegos, Miguel
Format: Article
Language:English
Subjects:
categorical properties of feedback actions
Feedback
Food science
Linear control
Linear systems
Vector spaces
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10122088