Some Categorical Properties of Linear Systems

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.