On the K-theory of feedback actions on linear systems

2013/06/05 by Miguel V. Carriegos, Carriegos, Miguel V., Ángel Luis Muñoz Castañeda +1
Mathematics · #13C10 #15A21 #93B10 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AC #math.KT #msc:13C10 #msc:15A21 #msc:93B10

paper · pdf · doi:10.48550/arxiv.1306.1021

20 pages

arxiv created 2013/06/05 · arxiv updated 2013/06/06

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 K₀ group of the (monoidal) category. Hence a link from linear dynamical systems to algebraic K-theory is stablished.

Related

• Feedback classification of linear systems over von Neumann regular rings
• Dynamics of linear control systems and stabilization
• Feedback Differential Invariants
• Classifications of Linear Controlled Systems
• Stabilizability with bounded feedback for analytic linear control systems