Non-local properties of non-linear systems, linear with respect to control function, are studied. We consider a class of such systems that are homogeneous at the origin. At a point different from the origin the system may be non-homogeneous, so its homogeneous approximation is of interest. However, at such points, the system may become less singular than at the origin. We describe a set of points where the system is as singular as at the origin. It is shown that such a set forms a linear subspace. The main tool used in the paper is a free algebra approach proposed in our previous papers.

中文翻译：

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齐次控制系统最大奇点子空间

研究了相对于控制函数呈线性的非线性系统的非局部性质。我们考虑一类这样的系统，它们在起源上是同质的。在与原点不同的点上，系统可能是不均匀的，因此它的均匀逼近很受关注。但是，在这样的点上，系统可能会变得比原始系统少。我们描述了一组点，其中系统与原点一样奇异。示出了这样的集合形成线性子空间。本文中使用的主要工具是我们先前论文中提出的自由代数方法。