RT info:eu-repo/semantics/article
T1 Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems
A1 Carriegos Vieira, Miguel
A2 Algebra
K1 Matemáticas
K1 Dynamic feedback
K1 Partitions
K1 Form
K1 1201 Álgebra
AB [EN] Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This additive category has a minimal exact structure and thus a notion of simple systems as those systems have no subsystems apart from zero and themselves. The so-called single-input systems are proven to be exactly the simple systems in the category of reachable systems over vector spaces. The category is also proven to be semisimple in objects because every reachable linear system is decomposed in a finite parallel gathering of simple systems. Hence, decomposition result is fulfilled for linear systems and feedback morphisms, but category of reachable linear systems is not abelian semisimple because it is not balanced and hence fails to be abelian. Finally, it is conjectured that the category of linear systems and feedback actions is in fact semiabelian; some threads to find the result and consequences are also given
PB Hindawi
SN 2314-4629
LK https://hdl.handle.net/10612/19284
UL https://hdl.handle.net/10612/19284
NO Carriegos. (2023). Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems. Journal of Mathematics, 2023. https://doi.org/10.1155/2023/7963973
DS BULERIA. Repositorio Institucional de la Universidad de León
RD 16-jun-2024