Mathematical Sciences: Systems Theory, Transfer Functions and Geometry

提出了用动态补偿方法解决定常线性控制系统的极点配置问题。一个目标是找到具有真实动态补偿器的极点放置映射上的充分和几乎必要条件，给出最小阶真实补偿器的精确界。另一种是研究与固定McMillan度的多变量线性系统空间相关的各种拓扑问题，从而对物理自然紧化进行比较分析。极点放置问题是线性系统理论中的一个基本问题。线性系统在许多应用场合中仍然很重要。

The principal investigator proposes to address the problem of pole placement by dynamic compensation for time-invariant linear control systems. One goal is to find sufficient and almost necessary conditions for the pole placemnt map with real dynamic compensators tobe onto, giving exact bounds for the minimal order real compensator. Another is to study various topological questions related to the space of multivariable linear systems with a fixed McMillan degree leading to a comparative analysis of physically natural compactifications. The pole placement problem is fundamental in linear systems theory. Linear systems remain important in many applied situations.