A characterization of von Neumann rings in terms of linear systems

DOI10.1016/j.laa.2016.01.019zbMath1338.13019OpenAlexW2277915051MaRDI QIDQ252621

Ángel Luis Muñoz Castañeda, Miguel V. Carriegos, Noemí DeCastro-García

Publication date: 3 March 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2016.01.019

zbMATH Keywords

linear systemsreachabilityvon Neumann regular ringsfeedback enumeration problemlocally Brunowsky

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Linear systems in control theory (93C05) Canonical structure (93B10) Pole and zero placement problems (93B55) Projective and free modules and ideals in commutative rings (13C10) Linear equations (linear algebraic aspects) (15A06) Canonical forms, reductions, classification (15A21) von Neumann regular rings and generalizations (associative algebraic aspects) (16E50)

Related Items (4)

State representations of convolutional codes over a finite ring ⋮ Partitions, Diophantine equations, and control systems ⋮ Feedback equivalence of convolutional codes over finite rings ⋮ A matrix based list decoding algorithm for linear codes over integer residue rings

Cites Work

• Uniform ensemble controllability for one-parameter families of time-invariant linear systems
• Rosenbrock's theorem for systems over von Neumann regular rings
• The computation of Kronecker's canonical form of a singular pencil
• Cyclic accessibility of reachable states characterizes von Neumann regular rings
• The pointwise feedback relation for linear dynamical systems
• On the local-global decomposition of linear control systems.
• Brunovsky's canonical form for linear dynamical systems over commutative rings
• Enumeration of classes of linear systems via equations and via partitions in an ordered Abelian monoid
• Feedback classification of linear systems over von Neumann regular rings
• Assignable polynomials to linear systems over von Neumann regular rings
• Discrete multidimensional systems over \(\mathbb Z _{n}\)
• THE REALIZATION PROBLEM FOR VON NEUMANN REGULAR RINGS
• Disturbance Decoupling of Boolean Control Networks
• Partitions of elements in a monoid and its applications to systems theory
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