A reachability test for systems over polynomial rings using Groebner bases

L.C.G.J.M. Habets

doi:10.23919/ACC.1993.4792842

A reachability test for systems over polynomial rings using Groebner bases

L.C.G.J.M. Habets

Mathematics and Computer Science

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/Congresprocedure › Conferentiebijdrage › Academic › peer review

2 Citaten (Scopus)

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Conditions for the reachability of a system over a polynomial ring are well known in the literature. However, verification of these conditions is in general a difficult problem. In this paper, the reachability problem is expressed in terms of polynomial ideals, and Groebner Bases are used to carry out the test explicitly. Four different methods are proposed, and their effectiveness is compared. With one of these methods, it is also possible to obtain a right- or left-inverse of a general non-square polynomial matrix, often required in the design of feedback compensators.

Originele taal-2	Engels
Titel	1993 American Control Conference
Plaats van productie	Piscataway
Uitgeverij	Institute of Electrical and Electronics Engineers
Pagina's	226-230
Aantal pagina's	5
ISBN van geprinte versie	0780308611
DOI's	https://doi.org/10.23919/ACC.1993.4792842
Status	Gepubliceerd - 1 dec. 1993
Evenement	1993 American Control Conference, ACC 1993 - San Francisco, Verenigde Staten van Amerika Duur: 2 jun. 1993 → 4 jun. 1993

Congres

Congres	1993 American Control Conference, ACC 1993
Land/Regio	Verenigde Staten van Amerika
Stad	San Francisco
Periode	2/06/93 → 4/06/93

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abstract = "Conditions for the reachability of a system over a polynomial ring are well known in the literature. However, verification of these conditions is in general a difficult problem. In this paper, the reachability problem is expressed in terms of polynomial ideals, and Groebner Bases are used to carry out the test explicitly. Four different methods are proposed, and their effectiveness is compared. With one of these methods, it is also possible to obtain a right- or left-inverse of a general non-square polynomial matrix, often required in the design of feedback compensators.",

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AB - Conditions for the reachability of a system over a polynomial ring are well known in the literature. However, verification of these conditions is in general a difficult problem. In this paper, the reachability problem is expressed in terms of polynomial ideals, and Groebner Bases are used to carry out the test explicitly. Four different methods are proposed, and their effectiveness is compared. With one of these methods, it is also possible to obtain a right- or left-inverse of a general non-square polynomial matrix, often required in the design of feedback compensators.

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ER -

A reachability test for systems over polynomial rings using Groebner bases

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