Module structure of constant linear systems and its applications to controllability
Module structure of constant linear systems and its applications to controllability
复制标题
常线性系统的模块结构及其在可控性中的应用
DOI：
10.1016/0022-247x(81)90133-5
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发表时间：
1981
影响因子：
1.3
通讯作者：
Y. Yamamoto
中科院分区：
文献类型：
--
作者：
Y. Yamamoto
我们将引入一个新的模块结构的一大类连续时间常数线性系统。这是作为有限维常数线性系统的经典k [z]-模结构的自然扩展来完成的。这个模作用被用来研究线性系统的能达性和能控性之间的关系。在引入Kamen [12]的K-能控性概念后，我们在第五节给出了如下结果：若一个常系数线性系统由泛函微分方程x ~（？）= Fx+ Gu描述，其中x和G属于Banach空间X，且G是K-能控到零的，则每个可达状态在有界时间内是可达和能控的。(The第5节给出的结果比这个更一般一些。）我们在第6节中也给出了一个简单的例子来说明这个结果。
We shall introduce a new module structure to a large class of continuous-time constant linear systems. This is done as a natural extension of the classical k [z]-module structure of finite-dimensional constant linear systems. This module action is used to investigate the relationship between reachability and controllability of linear systems. After introducing the notion of K-controllability due to Kamen [12], we give the following result in Section 5: If a constant linear system is described by a functional differential equation x ̇= Fx+ Gu, where x and G belong to a Banach space X, and if G is K-controllable to zero, then every reachable state is reachable and controllable in bounded time.(The result given in Section 5 is a little more general than this.) We also give a simple example in Section 6 to illustrate this result.