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In this paper, we consider issues relative to prescribed time stabilisationof a chain of integrators of arbitrary length, either pure (i.e., where thereis no disturbance) or perturbed. In a first part, we revisit the proportionalnavigation feedback (PNF) approach and we show that it can be appropriatelyrecasted within the framework of time-varying homogeneity. As a firstconsequence, we first recover all previously obtained results on PNF withsimpler arguments. We then apply sliding mode inspired feedbacks to achieveprescribed stabilisation with uniformly bounded gains. However, all thesefeedbacks are robust to matched uncertainties only. In a second part, weprovide a feedback law yet inspired by sliding mode which not only stabilisesthe pure chain of integrators in prescribed time but also exhibits somerobustness in the presence of measurement noise and unmatched uncertainties.

Stabilization for a perturbed chain of integrators in prescribed time