{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:19:37Z","timestamp":1787321977609,"version":"build-2736575974"},"reference-count":37,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>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 $D\\in\\mathbb{R}^n$.<\/jats:p>","DOI":"10.1137\/140997725","type":"journal-article","created":{"date-parts":[[2015,8,11]],"date-time":"2015-08-11T11:28:27Z","timestamp":1439292507000},"page":"2406-2423","source":"Crossref","is-referenced-by-count":8,"title":["$L_p$-Stabilization of Integrator Chains Subject to Input Saturation Using Lyapunov-Based Homogeneous Design"],"prefix":"10.1137","volume":"53","author":[{"given":"Yacine","family":"Chitour","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohamed","family":"Harmouche","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Salah","family":"Laghrouche","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,8,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.860314"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"V. 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Filippov,\n                      Differential Equations with Discontinuous Right-Hand Side\n                      , Kluwer, Dordrecht, Netherlands, 1998."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2041978"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1080\/00207176908905846"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012991221791"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TCST.2008.2002950"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2203056"},{"key":"atypb13","first-page":"2035","volume":"87","author":"Harmouche M.","journal-title":"Internat. J. Control"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(02)00119-6"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-012-9672-8"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-22164-4_2"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(02)00125-1"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(95)99124-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(95)00176-X"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1109\/9.618237"},{"key":"atypb21","unstructured":"Z. Lin,\n                      Low Gain Feedback\n                      , Springer, Berlin, 1998."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012994263469"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"M. Malisoff and F. Mazenc,\n                      Construction of Strict Lyapunov Functions\n                      , Comm. Control Engrg., Springer-Verlag, Berlin, 2009.","DOI":"10.1007\/978-1-84882-535-2"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2004.05.018"},{"key":"atypb25","first-page":"435","volume":"96","author":"Megretski A.","year":"1996","journal-title":"Proceedings of IFAC"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2011.2171170"},{"key":"atypb27","unstructured":"E. P. Ryan,\n                      Optimal Relay and Saturating Control System Synthesis\n                      , Institution of Electrical Engineers, London, 1982."},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1109\/9.863591"},{"key":"atypb29","first-page":"163","author":"Sontag E. D.","year":"2007","journal-title":"Berlin"},{"key":"atypb30","unstructured":"E. D. Sontag,\n                      Mathematical Control Theory: Deterministic Finite Dimensional Systems\n                      , 2nd ed., Texts in Appl. 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