Assignable polynomials to linear systems over von Neumann regular rings

被引:2
|
作者
Saez-Schwedt, A. [1 ]
机构
[1] Univ Leon, Dept Matemat, E-24071 Leon, Spain
关键词
Systems over commutative rings; Commutative von Neumann regular rings; Polynomials assignable by state feedback; CONVOLUTIONAL-CODES;
D O I
10.1016/j.laa.2014.04.029
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a system (A, B) over a commutative von Neumann regular ring R, it is proved that there exist a matrix F and a vector u such that the single-input system (A + BF, Bu) and the original system (A, B) have the same module of reachable states and the same set of polynomials assignable by state feedback. Moreover, there is a bijection between reachable states and assignable polynomials, in the form of a certain isomorphism of R-modules, and the existence of this isomorphism for all systems actually characterizes von Neumann regular rings. Finally, the set of assignable polynomials to a single-input system is completely described for arbitrary commutative rings, which in the case of von Neumann regular rings completes the study of assignable polynomials to multi-input systems. (C) 2014 Elsevier Inc. All rights reserved.
引用
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页码:104 / 119
页数:16
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