On the K-theory of feedback actions on linear systems

A categorical approach to linear control systems is introduced. Feedback actions on linear control systems arise as symmetric monodical category SR. Stable feedback isomorphisms generalize dynamic enlargement of pairs of matrices. Subcategory of locally Brunovsky linear systems BR is studied. We prove that the stable feedback isomorphisms of locally Brunovsky linear systems are characterized by the Grothendieck group K0(BR). Hence a link from linear dynamical systems to algebraic K-theory is established.