The lattice of minimal realizations of response maps over rings

Eduardo D. Sontag

doi:10.1007/BF01768475

The lattice of minimal realizations of response maps over rings

Eduardo D. Sontag

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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 language	English (US)
Pages (from-to)	169-175
Number of pages	7
Journal	Mathematical Systems Theory
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/BF01768475
State	Published - Dec 1977

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Mathematics(all)
Computational Theory and Mathematics

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10.1007/BF01768475

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title = "The lattice of minimal realizations of response maps over rings",

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.",

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AB - 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.

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The lattice of minimal realizations of response maps over rings

Abstract

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