On the K-theory of feedback actions on linear systems
Miguel V. Carriegos, \'Angel Luis Mu\~noz Casta\~neda
TL;DR
This paper introduces a categorical framework for linear control systems, linking feedback actions to algebraic K-theory, and characterizes stable feedback isomorphisms using K_0 groups.
Contribution
It develops a novel categorical approach to linear control systems, connecting feedback actions with algebraic K-theory and characterizing isomorphisms via K_0 groups.
Findings
Feedback actions form a symmetric monoidal category.
Stable feedback isomorphisms are characterized by K_0 groups.
A link between linear systems and algebraic K-theory is established.
Abstract
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.
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