交换环上线性系的初等因子和约化子式
Elementary Factors and Reduced Minors for Linear Systems over Commutative Rings
摘要：
1994年，Sule利用初等因子和约化子式给出了唯一分解域上系统反馈可镇定的充要条件.最近，Mori和Abe将他的理论推广到交换环上。他们引入了广义初等因子的概念，它是初等因子的推广，并给出了反馈可镇定的充要条件。本文给出了约化子式的两个推广。利用它们，我们给出了交换环上反馈可镇定的充要条件。进一步给出了广义化与广义初等因子之间的关系。
英文摘要：
In 1994, Sule presented the necessary and sufficient conditions of the feedback stabilizability of systems over unique factorization domains in terms of elementary factors and in terms of reduced minors. Recently, Mori and Abe have generalized his theory over commutative rings. They have introduced the notion of the generalized elementary factor, which is a~generalization of the elementary factor, and have given the necessary and sufficient condition of the feedback stabilizability. In this paper, we present two generalization of the reduced minors. Using each of them, we state the necessary and sufficient condition of the feedback stabilizability over commutative rings. Further we present the relationship between the generalizations and the generalized elementary factors.
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