Pseudo-rational input/output maps and their realizations: a fractional representation approach to in
Pseudo-rational input/output maps and their realizations: a fractional representation approach to in
复制标题
伪有理输入/输出映射及其实现：一种分数表示方法
DOI：
10.1137/0326081
复制
发表时间：
1988
影响因子：
2.2
通讯作者：
Y. Yamamoto
中科院分区：
文献类型：
--
作者：
Y. Yamamoto
本文研究了一类无限维线性系统脉冲响应的矩阵分式表示，其中特别包括时滞微分系统。本文称这种脉冲响应为伪有理脉冲响应。这种分数表示被有效地用于从抽象的移位实现导出具体的函数空间模型。给定一个分数表示Q^{-1} * P$，一个类似于有限维系统的Fuhrmann实现的标准可观测实现与之相联系，引入了一个新的互质性概念，称为近似左互质性，并且证明了与表示$Q^{-1} * P$相关联的标准可观测实现是正则的当且仅当Q和P近似左互质。一些例子进行了讨论，以说明各种互质性的概念，已经出现在文献中的关系。
This paper studies matrix fractional representation for impulse responses of a certain class of infinite-dimensional linear systems which contains, in particular, delay-differential systems. Such impulse responses are called pseudo-rational in this paper. This fractional representation is effectively used to derive concrete function space models from the abstract shift realizations. Given a fractional representation $Q^{ - 1} * P$, a standard observable realization, analogous to Fuhrmann realizations for finite-dimensional systems, is associated to it. A new notion of coprimeness called approximate left coprimeness is introduced, and it is shown that the standard observable realization associated to the representation $Q^{ - 1} * P$ is canonical if and only if Q and P are approximately left coprime. Some examples are discussed to illustrate the relationships among various coprimeness concepts that have appeared in the literature.