Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This has a minimal exact structure thus notion simple as those have no subsystems apart from zero themselves. The so-called single-input are proven to be exactly in reachable spaces. is also semisimple objects because every system decomposed finite Hence, decomposition result fulfilled for morphisms, but not abelian it balanced hence fails abelian. Finally, conjectured that actions fact semiabelian; some threads find consequences given.