On the \(K\)-theory of feedback actions on linear systems. (English) Zbl 1302.93070
Summary: A categorical approach to linear control systems is introduced. Feedback actions on linear control systems arise as symmetric monodical category \(S_R\). Stable feedback isomorphisms generalize dynamic enlargement of pairs of matrices. Subcategory of locally Brunovsky linear systems \(B_R\) is studied. We prove that the stable feedback isomorphisms of locally Brunovsky linear systems are characterized by the Grothendieck group \(K_0(B_R)\). Hence a link from linear dynamical systems to algebraic \(K\)-theory is established.
MSC:
| 93B25 | Algebraic methods |
| 19A49 | \(K_0\) of other rings |
| 13C60 | Module categories and commutative rings |
| 16E20 | Grothendieck groups, \(K\)-theory, etc. |
Keywords:
feedback equivalence; commutative ring; dynamic enlargement; stable equivalence; \(K\)-theory invariantReferences:
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