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Stabilization for a Perturbed Chain of Integrators in Prescribed Time

Yacine Chitour 1 Rosane Ushirobira 2 Hassan Bouhemou 3
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : 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.
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Submitted on : Tuesday, October 13, 2020 - 10:23:36 AM
Last modification on : Wednesday, September 1, 2021 - 3:30:17 AM
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Yacine Chitour, Rosane Ushirobira, Hassan Bouhemou. Stabilization for a Perturbed Chain of Integrators in Prescribed Time. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2020, ⟨10.1137/19M1285937⟩. ⟨hal-02964839⟩



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