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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.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, 08903, New Brunswick, N.J., USA

    Eduardo D. Sontag

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  1. Eduardo D. Sontag
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Additional information

This research was supported in part by US Army Research Grant DA-ARO-D-31-124-72-G114 and by US Air Force Grant 72-2268 through the Center for Mathematical System Theory, University of Flroida, Gainesville, FL 32611, USA.

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Sontag, E.D. The lattice of minimal realizations of response maps over rings. Math. Systems Theory 11, 169–175 (1977). https://doi.org/10.1007/BF01768475

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  • DOI: https://doi.org/10.1007/BF01768475

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