%0 Journal Article %T Lp-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design. %+ Laboratoire des signaux et systèmes (L2S) %A Chitour, Yacine %A Harmouche, M. %A Laghrouche, Salah %< avec comité de lecture %@ 0363-0129 %J SIAM Journal on Control and Optimization %I Society for Industrial and Applied Mathematics %V 53 %N 4 %P 2406-2423 %8 2015 %D 2015 %R 10.1137/140997725 %Z Computer Science [cs]/Automatic Control Engineering %Z Engineering Sciences [physics]/AutomaticJournal articles %X Consider the $n$th integrator $\dot x=J_nx+\sigma(u)e_n$, where $x\in\mathbb{R}^n$, $u\in\mathbb{R}$, $J_n$ is the $n$th Jordan block and $e_n=(0\ \cdots 0\ 1)^T\in\mathbb{R}^n$. We provide easily implementable state feedback laws $u=k(x)$ which not only render the closed-loop system globally asymptotically stable but also are finite-gain $L_p$-stabilizing with arbitrarily small gain, as in [A. Saberi, P. Hou, and A. Stoorvogel, IEEE Trans. Automat. Control, 45 (2000), pp. 1042--1052]. These $L_p$-stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite-time stabilization of linear systems. We also provide additional $L_\infty$-stabilization results for the case of both internal and external disturbances of the $n$th integrator, namely, for the perturbed system $\dot x=J_nx+e_n\sigma (k(x)+d)+D$, where $d\in\mathbb{R}$ and $D\in\mathbb{R}^n$. %G English %2 https://centralesupelec.hal.science/hal-01271283/document %2 https://centralesupelec.hal.science/hal-01271283/file/pdf_de_lp_stabilization_of_integrator.pdf %L hal-01271283 %U https://centralesupelec.hal.science/hal-01271283 %~ CNRS %~ UNIV-PSUD %~ SUP_LSS %~ SUP_SYSTEMES %~ CENTRALESUPELEC %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ UNIV-PSUD-SACLAY %~ CENTRALESUPELEC-SACLAY %~ GS-COMPUTER-SCIENCE %~ TEST3-HALCNRS