<p style='text-indent:20px;'>In this paper, we study some non-negative integers related to a linear time varying system and to some Krylov sub-spaces associated to this system. Such integers are similar to the controllability indices and have been used in the literature to derive results on the controllability of linear systems. The purpose of this paper goes in the same direction by studying the local behavior of these integers especially nearby instants in the time interval with some maximal rank condition and then apply them to get some results which generalize the mentioned existing results.</p>

中文翻译：

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线性时变系统的局部卡尔曼等级条件

<p style='text-indent:20px;'>在本文中，我们研究了一些与线性时变系统相关的非负整数以及与该系统相关的一些 Krylov 子空间。这种整数类似于可控性指数，并已在文献中用于推导线性系统可控性的结果。本文的目的与此相同，通过研究这些整数的局部行为，特别是在具有最大秩条件的时间间隔内的附近瞬间，然后将它们应用到一些结果，从而推广上述现有结果。</p>