  A categorical approach to linear control systems is introduced. Feedback
actions on linear systems arises as a symmetric monoidal category. Stable
feedback isomorphisms generalize enlargement of pairs of matrices. Subcategory
of locally Brunovsky linear systems is studied and the stable feedback
isomorphisms of locally Brunovsky linear systems are characterized by the K_0
group of the (monoidal) category. Hence a link from linear dynamical systems to
algebraic K-theory is stablished.
