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

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

2 Citations (Scopus)

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.

Original language	English
Title of host publication	1993 American Control Conference
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	226-230
Number of pages	5
ISBN (Print)	0780308611
DOIs	https://doi.org/10.23919/ACC.1993.4792842
Publication status	Published - 1 Dec 1993
Event	1993 American Control Conference, ACC 1993 - San Francisco, United States Duration: 2 Jun 1993 → 4 Jun 1993

Conference

Conference	1993 American Control Conference, ACC 1993
Country/Territory	United States
City	San Francisco
Period	2/06/93 → 4/06/93

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10.23919/ACC.1993.4792842

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title = "A reachability test for systems over polynomial rings using Groebner bases",

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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T2 - 1993 American Control Conference, ACC 1993

Y2 - 2 June 1993 through 4 June 1993

ER -

A reachability test for systems over polynomial rings using Groebner bases

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