本课程讲授与控制理论研究有关的现代数学，以及这些知识如何应用到控制系统分析与设计的。内容包括：代数学（集合、群、环、域），公理化科学，线性系统的变换群，传递函数矩阵的多项式分解；泛函分析（拓扑基础、度量空间、BANACH空间、HILBERT空间），系统响应的唯一性，有界与稳定，系统辨识的数学基础。课程用英语授课，和英语回答问题。

The course is about the mathematical foundations of Mordern Control Theory. It includes Algebra and Functional Analysis. In algebra part, we deal with the basic algebra that includes sets, groups, rings, and fields as well as the transformation group of a linear system, the polynomial decomposition of a transfer function matrix. The functional analysis includes the basic topology, metric spaces, Banach spaces and Hilbert spaces. we deal with the uniqueness of system's response, boundedness and stability, and the theory of identification.