SIAM Journal on Control and Optimization, Volume 58, Issue 2, Page 1022-1048, January 2020.
In this paper, we consider issues relative to prescribed-time stabilization of a chain of integrators of arbitrary length, either pure (i.e., where there is no disturbance) or perturbed. In the first part, we revisit the proportional navigation feedback (PNF) approach, and we show that it can be appropriately recasted within the framework of time-varying homogeneity. As a first consequence, we recover all previously obtained results on PNF with simpler arguments. We then apply sliding mode--inspired feedbacks to achieve prescribed stabilization with uniformly bounded gains. However, all these feedbacks are robust to matched uncertainties only. In the second part, we provide another sliding mode--inspired feedback which not only stabilizes the pure chain of integrators in prescribed time but also exhibits some robustness in the presence of measurement noise and unmatched uncertainties.

中文翻译：

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规定时间内扰动积分器链的稳定性

SIAM控制与优化杂志，第58卷，第2期，第1022-1048页，2020年1月。
在本文中，我们考虑与任意长度的纯净（即，无扰动）或扰动的积分器的规定时间稳定有关的问题。在第一部分中，我们重新审视了比例导航反馈（PNF）方法，并证明了它可以在时变同质性的框架内适当地重铸。首先，我们使用更简单的参数恢复了先前在PNF上获得的所有结果。然后，我们应用滑模激励的反馈，以达到均匀稳定增益的规定稳定性。但是，所有这些反馈仅对匹配的不确定性具有鲁棒性。在第二部分中