This paper shows that within the space of all LTI systems, equipped with the Zariski topology, the set of impulse controllable systems contains an open dense set of systems; in other words, impulse controllable systems are generic. This genericity persists for many closed subsets of LTI systems of interest, such as the class of singular descriptor systems.

中文翻译：

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脉冲可控性的持久性

本文表明，在所有具有Zariski拓扑结构的LTI系统的空间中，脉冲可控系统集包含一个开放的密集系统集；换句话说，脉冲可控系统是通用的。这种通用性对于感兴趣的LTI系统的许多封闭子集（例如奇异描述符系统的类）仍然存在。