Although realizations of transfer functions are a standard topic in textbooks about linear systems theory, this article focuses on several points that are not widely treated. First, it is shown that, for a given dynamics matrix A, the smallest number of sensors and actuators that can be used to form a minimal realization is determined by properties of the Jordan form of A. This leads to the notions of minimally sensed and minimally actuated systems. Next, the rank of a transfer function is related to properties of the Jordan form of A and the rank of the Rosenbrock system matrix.

中文翻译：

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重温最小实现[讲座笔记]


尽管传递函数的实现是线性系统理论教科书中的标准主题，但本文重点讨论了几个没有被广泛讨论的点。首先，它表明，对于给定的动态矩阵 A，可用于形成最小实现的传感器和执行器的最小数量由 A 的 Jordan 形式的属性决定。这导致了最小感测和最小感测的概念。最小驱动系统。接下来，传递函数的秩与 A 的 Jordan 形式的属性和 Rosenbrock 系统矩阵的秩相关。