Pole assignability in polynomial rings, power series rings, and Prüfer domains

Brewer, J. W.; Katz, Daniel J.; Ullery, William

doi:10.1016/0021-8693(87)90031-7

Cited by 40 publications

(10 citation statements)

References 14 publications

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“…We have just said that the stacked bases property implies the UCS-property. The converse holds for Prüfer domains: Proposition 2.3 [1] (see also [6,Thm 4.8…”

Section: The Ucs-propertymentioning

confidence: 96%

Does Int $${(\mathbb {Z})}$$ have the stacked bases property?

Chabert

2012

Arab. J. Math.

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“…We have just said that the stacked bases property implies the UCS-property. The converse holds for Prüfer domains: Proposition 2.3 [1] (see also [6,Thm 4.8…”

Section: The Ucs-propertymentioning

confidence: 96%

Does Int $${(\mathbb {Z})}$$ have the stacked bases property?

Chabert

2012

Arab. J. Math.

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“…We say that a ring R is UCU (Unit-content Contains Unimodular) if, whenever U 1 (B) = R, there exists a vector u with Bu unimodular, see [1]. …”

Section: U1 U2mentioning

confidence: 99%

“…with residual rank zero is trivially 1-cyclizable, so we may assume that res.rk(Σ) = 1, i.e., the ideal generated by ( [1]) is reachable, and hence, Σ is 1-cyclizable.…”

Section: U1 U2mentioning

confidence: 99%

“…For this, let R be an FC ring and (A, B) a reachable system over R. The existence of a reachable system (A + BK, Bu) forces u to be a unimodular vector. Since FC rings are GCU rings [1], unimodular vectors can be completed to invertible matrices. (iii) R is a UCU ring with the strong FC s property.…”

Section: Then (I)⇔(ii)⇒(iii) and If S = 1 Then All Conditions Are Ementioning

confidence: 99%

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Matricial decomposition of systems over rings

Sáez-Schwedt

2008

ELA

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Abstract. This paper extends to non-controllable linear systems over rings the property FC s (s > 0), which means "feedback cyclization with s inputs": given a controllable system (A, B), there exist a matrix K and a matrix U with s columns such that (A + BK, BU ) is controllable. Clearly, FC 1 is the usual FC property. The main technique used in this work is the obtention of block decompositions for systems, with controllable subsystems of a certain size. Each of the studied decompositions is associated to a class of commutative rings for which all systems can be decomposed accordingly. Finally, examples are shown of FC s rings (for s > 1) which are not FC rings.

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“…Several recent papers have been concerned with PA-and BCS-rings: e.g. [1,2,4,6,7]. Among the more important results in this area is the following of Hautus and Sontag.…”

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confidence: 99%