On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains

Yves Rouchaleau; Eduardo D. Sontag

doi:10.1016/0022-0000(79)90052-7

On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains

Yves Rouchaleau, Eduardo D. Sontag

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23 Scopus citations

Abstract

This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can be always obtained, and the result is applied to delay-differential systems.

Original language	English (US)
Pages (from-to)	65-75
Number of pages	11
Journal	Journal of Computer and System Sciences
Volume	18
Issue number	1
DOIs	https://doi.org/10.1016/0022-0000(79)90052-7
State	Published - Feb 1979

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Networks and Communications
Computational Theory and Mathematics
Applied Mathematics

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10.1016/0022-0000(79)90052-7

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title = "On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains",

abstract = "This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can be always obtained, and the result is applied to delay-differential systems.",

author = "Yves Rouchaleau and Sontag, {Eduardo D.}",

note = "Funding Information: * This research was supported in part by U.S. Army Research Grant DAH CO4-74-G-0153 and U.S. Air Force Grant AFOSR 72-2268 through the Center for Mathematical System Theory, University of Florida, Gainesville, Fla. 32611.",

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N1 - Funding Information: * This research was supported in part by U.S. Army Research Grant DAH CO4-74-G-0153 and U.S. Air Force Grant AFOSR 72-2268 through the Center for Mathematical System Theory, University of Florida, Gainesville, Fla. 32611.

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N2 - This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can be always obtained, and the result is applied to delay-differential systems.

AB - This paper studies the problem of obtaining minimal realizations of linear input/output maps defined over rings. In particular, it is shown that, contrary to the case of systems over fields, it is in general impossible to obtain realizations whose dimension equals the rank of the Hankel matrix. A characterization is given of those (Noetherian) rings over which realizations of such dimensions can be always obtained, and the result is applied to delay-differential systems.

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On the existence of minimal realizations of linear dynamical systems over Noetherian integral domains

Abstract

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