In this paper, a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems is proposed. The class under consideration is the linear time-varying (LTV) class with time-varying integrable system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets, which results in convergent under-approximations in the sense of the Hausdorff distance. As a consequence of the convergence, it is shown that interior points of reachable sets are attainable using piecewise constant inputs. The computational complexity of a zonotopic implementation of the proposed method is discussed and comparisons with existing under-approximation methods are established. Finally, the proposed approach is illustrated through two numerical examples.

本文提出了一种对一类连续时间线性不确定系统的有限时间可及集和管进行逼近的方法。所考虑的类别是线性时变（LTV）类别，具有时变可积分系统矩阵，并且不确定的初始值和输入值属于已知的凸紧集。所提出的方法取决于对恒定输入可达集的迭代使用，这会导致在Hausdorff距离的意义上收敛的欠逼近。收敛的结果表明，使用分段常数输入可以达到可到达集合的内部点。讨论了所提出方法的区域局部实现的计算复杂性，并与现有的欠逼近方法进行了比较。最后，