{"paper":{"title":"$L_p$-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Mohamed Harmouche, Salah Laghrouche, Yacine Chitour","submitted_at":"2014-11-23T16:23:48Z","abstract_excerpt":"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. 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 o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6262","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}