The lattice of minimal realizations of response maps over rings

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Abstract

A lattice characterization is given for the class of minimal-rank realizations of a linear response map defined over a (commutative) Noetherian integral domain. As a corollary, it is proved that there are only finitely many nonisomorphic minimal-rank realizations of a response map over the integers, while for delay-differential systems these are classified by a lattice of subspaces of a finite-dimensional real vector space.

Original languageEnglish (US)
Pages (from-to)169-175
Number of pages7
JournalMathematical Systems Theory
Volume11
Issue number1
DOIs
StatePublished - Dec 1977

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics

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