Row reduced representations of behaviors over finite rings

Margreta Kuijper; Raquel Pinto; Jan W. Polderman

doi:10.1109/CDC.2007.4434686

Row reduced representations of behaviors over finite rings

Margreta Kuijper, Raquel Pinto, Jan W. Polderman

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form $\mathbb{Z}_{p^r}$, where $p$ is a prime number. Using a restricted calculus within $\mathbb{Z}_{p^r}$ we derive a meaningful and computable notion of row-reducedness.

Original language	Undefined
Title of host publication	Proceedings of the 46th IEEE Conference on Decision and Control
Place of Publication	United States
Publisher	IEEE
Pages	470-475
Number of pages	6
ISBN (Print)	1-4244-1498-9
DOIs	https://doi.org/10.1109/CDC.2007.4434686
Publication status	Published - 2007
Event	46th IEEE Conference on Decision and Control, CDC 2007 - Hilton New Orleans Riverside, New Orleans, United States Duration: 12 Dec 2007 → 14 Dec 2007 Conference number: 46

Publication series

Name
Publisher	IEEE
Number	7
ISSN (Print)	0024-3795
ISSN (Electronic)	1873-1856

Conference

Conference	46th IEEE Conference on Decision and Control, CDC 2007
Abbreviated title	CDC
Country/Territory	United States
City	New Orleans
Period	12/12/07 → 14/12/07

Keywords

Linear systems
finite rings
polynomial matrices
kernel representations
METIS-245955
row reduced
EWI-11750
IR-64588
Behaviors
predictable degree property

Access to Document

10.1109/CDC.2007.4434686

Cite this

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title = "Row reduced representations of behaviors over finite rings",

abstract = "Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form $\mathbb{Z}_{p^r}$, where $p$ is a prime number. Using a restricted calculus within $\mathbb{Z}_{p^r}$ we derive a meaningful and computable notion of row-reducedness.",

keywords = "Linear systems, finite rings, polynomial matrices, kernel representations, METIS-245955, row reduced, EWI-11750, IR-64588, Behaviors, predictable degree property",

author = "Margreta Kuijper and Raquel Pinto and Polderman, {Jan W.}",

note = "10.1109/CDC.2007.4434686 ; 46th IEEE Conference on Decision and Control, CDC 2007 ; Conference date: 12-12-2007 Through 14-12-2007",

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doi = "10.1109/CDC.2007.4434686",

language = "Undefined",

isbn = "1-4244-1498-9",

publisher = "IEEE",

number = "7",

pages = "470--475",

booktitle = "Proceedings of the 46th IEEE Conference on Decision and Control",

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Kuijper, M, Pinto, R & Polderman, JW 2007, Row reduced representations of behaviors over finite rings. in Proceedings of the 46th IEEE Conference on Decision and Control., 10.1109/CDC.2007.4434686, IEEE, United States, pp. 470-475, 46th IEEE Conference on Decision and Control, CDC 2007, New Orleans, Louisiana, United States, 12/12/07. https://doi.org/10.1109/CDC.2007.4434686

TY - GEN

T1 - Row reduced representations of behaviors over finite rings

AU - Kuijper, Margreta

AU - Pinto, Raquel

AU - Polderman, Jan W.

N1 - Conference code: 46

PY - 2007

Y1 - 2007

N2 - Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form $\mathbb{Z}_{p^r}$, where $p$ is a prime number. Using a restricted calculus within $\mathbb{Z}_{p^r}$ we derive a meaningful and computable notion of row-reducedness.

AB - Row reduced representations of behaviors over fields posses a number of useful properties. Perhaps the most important feature is the predictable degree property. This property allows a finite parametrization of the module generated by the rows of the row reduced matrix with prior computable bounds. In this paper we study row-reducedness of representations of behaviors over rings of the form $\mathbb{Z}_{p^r}$, where $p$ is a prime number. Using a restricted calculus within $\mathbb{Z}_{p^r}$ we derive a meaningful and computable notion of row-reducedness.

KW - Linear systems

KW - finite rings

KW - polynomial matrices

KW - kernel representations

KW - METIS-245955

KW - row reduced

KW - EWI-11750

KW - IR-64588

KW - Behaviors

KW - predictable degree property

U2 - 10.1109/CDC.2007.4434686

DO - 10.1109/CDC.2007.4434686

M3 - Conference contribution

SN - 1-4244-1498-9

SP - 470

EP - 475

BT - Proceedings of the 46th IEEE Conference on Decision and Control

PB - IEEE

CY - United States

T2 - 46th IEEE Conference on Decision and Control, CDC 2007

Y2 - 12 December 2007 through 14 December 2007

ER -