Polynomial rings over arbitrary fields in two or more variables are not pole assignable

DOI10.1016/0167-6911(82)90005-6zbMath0505.93027OpenAlexW2052649411MaRDI QIDQ1836637

Allen Tannenbaum

Publication date: 1982

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6911(82)90005-6

zbMATH Keywords

elliptic curvesreachabilitybranch pointsprojective idealscoefficient assignabilitypole assignabilitysystems over polynomial rings

Mathematics Subject Classification ID

Controllability (93B05) Pole and zero placement problems (93B55) Algebraic methods (93B25) Elliptic curves (14H52) Polynomials over commutative rings (13B25)

Related Items (11)

Pole assignability in polynomial rings, power series rings, and Prüfer domains ⋮ Pole shifting for families of systems: The dimension one case ⋮ BCS rings ⋮ New results on pole-shifting for parametrized families of systems ⋮ Polynomial rings which are BCS rings ⋮ ON POLE ASSIGNABILITY AND FEEDEBACK CYCLISATION FOR SYSTEMS OVER RINGS OF FINITE DIMENSION ⋮ Polynomial rings that are Bcs-rings ⋮ Three-dimensional feedback cyclization over \({\mathbb{C}}[y\)] ⋮ Comments on pole assignability over rings ⋮ The pole assignability property in polynomial rings over GCD-domains ⋮ On pole assignment problems in polynomial rings

Cites Work

• Unnamed Item
• Remarks on the pole-shifting problem over rings
• On pole assignability over polynomial rings
• Ring models for delay-differential systems
• On split realizations of response maps over rings

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