Algebraic system theory: an analyst's point of view
Algebraic system theory: an analyst's point of view
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代数系统论：分析师的观点
DOI：
10.1016/0016-0032(76)90076-4
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发表时间：
1976
影响因子：
4.1
通讯作者：
P. Fuhrmann
中科院分区：
文献类型：
--
作者：
P. Fuhrmann
相关的代数思想的研究线性系统已被确认和强调卡尔曼在各种出版物最终在他出色的论述在第四部分的参考文献。（八）、本文是对这一部分重新解读的结果。毫无疑问，这是一个最优秀的成就，在数学系统理论和看来，卡尔曼的承认模块结构的基本结构，在线性系统理论必将最终成为标准的方式阐述的问题。（就作者个人而言，这本书在很大程度上归功于这本书，因为第一次阅读它引起了他对系统理论的兴趣。）有什么可以添加到卡尔曼的论述，可以抛出一些更多的光在一个有据可查的主题？似乎有一个遗漏在一个重要的方向，因为没有足够的接触是与罗森布罗克的办法，线性系统理论（1）。事实上，在（1）中起如此重要作用的互质因子分解在（3）中根本没有出现。本文的目的是产生一种方法，它将综合卡尔曼的代数方法，状态空间方法以及Rosenbrock.The多项式矩阵方法的需要，这样一个综合已经认识到Eckberg在他的博士论文（2），本文有很多共同的想法介绍了那里。不同之处主要在于Eckberg通过选择规范矩阵来强调唯一性，而我们尽可能采取更抽象和无坐标的路线。根据状态空间同构定理的哲学，我们只剩下模相似性的唯一性。
The relevance of algebraic ideas in the study of linear systems has been recognized and stressed by Kalman in various publications culminating in his excellent exposition in Part Four of Ref.(8). This paper is the result of a re-reading of that part. No doubt this is one of the finest achievements in Mathematical System Theory and it seems that Kalman’s recognition of the module structure as the basic structure in linear system theory is bound eventually to become the standard way of exposition for the subject.(Personally this author owes a great deal to this book as the first reading of it aroused his interest in System Theory.) What is there to add to Kalman’s exposition which could throw some more light on a well-documented subject? It seems that there is an omission in one important direction inasmuch as not sufficient contact is made with Rosenbrock’s approach to linear system theory (1). In fact the coprime factorizations playing such an important role in (1) do not appear at all in (3). The aim of this paper is to produce an approach which would synthesize the algebraic approach of Kalman, the state space approach as well as the polynomial matrix methods of Rosenbrock.The need for such a synthesis has been recognized by Eckberg in his doctoral thesis (2) and this paper has a lot in common with the ideas introduced there. The differences are mainly in that Eckberg emphasizes uniqueness via a choice of canonical matrices whereas we take a more abstract and coordinate free route whenever possible. We are left with uniqueness modulo similarity in line with the philosophy of the state space isomorphism theorem.