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Some Categorical Properties of Linear Systems

Author

Listed:
  • Miguel V. Carriegos

    (Departamento of Matemáticas, Universidad de León, 24071 León, Spain)

Abstract

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.

Suggested Citation

  • Miguel V. Carriegos, 2022. "Some Categorical Properties of Linear Systems," Mathematics, MDPI, vol. 10(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2088-:d:840256
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