{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T02:08:46Z","timestamp":1778897326453,"version":"3.51.4"},"reference-count":50,"publisher":"Elsevier BV","issue":"8","license":[{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100010040","name":"Taishan Scholar Project of Shandong Province","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010040","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773073"],"award-info":[{"award-number":["61773073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of the Franklin Institute"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.jfranklin.2026.108652","type":"journal-article","created":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T06:05:29Z","timestamp":1776233129000},"page":"108652","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Finite-time stabilization of low-order stochastic feedforward systems with general power structure via output feedback control"],"prefix":"10.1016","volume":"363","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2434-1040","authenticated-orcid":false,"given":"Liang","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-3207-7502","authenticated-orcid":false,"given":"Gang","family":"Sun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6611-3265","authenticated-orcid":false,"given":"Rulan","family":"Bai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jfranklin.2026.108652_bib0001","series-title":"Stabilization of Nonlinear Uncertain Systems","author":"Krstic","year":"1998"},{"key":"10.1016\/j.jfranklin.2026.108652_bib0002","series-title":"Stochastic Differential Equations and Applications","author":"Mao","year":"2007"},{"key":"10.1016\/j.jfranklin.2026.108652_bib0003","series-title":"Stochastic Stability of Differential Equations","author":"Khasminskii","year":"2012"},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108652_bib0004","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1137\/S0363012996307059","article-title":"Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion","volume":"37","author":"Pan","year":"1999","journal-title":"SIAM J. Contr. Optim."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108652_bib0005","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0167-6911(97)00068-6","article-title":"Stochastic nonlinear stabilization-I: a backstepping design","volume":"32","author":"Deng","year":"1997","journal-title":"Syst. Contr. Lett."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0006","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1002\/rnc.1255","article-title":"Output-feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states","volume":"18","author":"Liu","year":"2008","journal-title":"Int. J. Robust Nonlinear Contr."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108652_bib0007","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1016\/j.automatica.2008.12.002","article-title":"Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching","volume":"45","author":"Wu","year":"2009","journal-title":"Automatica"},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108652_bib0008","doi-asserted-by":"crossref","first-page":"10542","DOI":"10.1109\/TCYB.2021.3069587","article-title":"Adaptive optimized backstepping control-based RL algorithm for stochastic nonlinear systems with state constraints and its application","volume":"52","author":"Li","year":"2022","journal-title":"IEEE Trans. Cybern."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0009","doi-asserted-by":"crossref","first-page":"3798","DOI":"10.1109\/TAC.2022.3201032","article-title":"Stabilization of triangular nonlinear systems with multiplicative stochastic state sensing noise","volume":"68","author":"Li","year":"2023","journal-title":"IEEE Trans. Automat. Contr."},{"issue":"9","key":"10.1016\/j.jfranklin.2026.108652_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2024.106867","article-title":"Adaptive output feedback control of stochastic systems with mismatched uncertainties input-output quantization","volume":"361","author":"Chen","year":"2024","journal-title":"J. Franklin Inst."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108652_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2024.107383","article-title":"Prescribed tracking of stochastic nonlinear systems with indifferentiable non-affine terms and dead zone","volume":"362","author":"Li","year":"2025","journal-title":"J. Franklin Inst."},{"key":"10.1016\/j.jfranklin.2026.108652_bib0012","series-title":"Constructive Nonlinear Control","author":"Sepulchre","year":"1997"},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108652_bib0013","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1016\/S0005-1098(02)00279-0","article-title":"Tracking trajectories of the cart-pendulum system","volume":"39","author":"Mazenc","year":"2003","journal-title":"Automatica"},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108652_bib0014","doi-asserted-by":"crossref","first-page":"3484","DOI":"10.1109\/TAC.2018.2882479","article-title":"Stabilization of uncertain feedforward nonlinear systems with application to underactuated systems","volume":"64","author":"Ye","year":"2019","journal-title":"IEEE Trans. Automat. Contr."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108652_bib0015","first-page":"1450","article-title":"Global prescribed-time stabilization for a class of uncertain feedforward nonlinear systems","volume":"70","author":"Zhang","year":"2023","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108652_bib0016","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1016\/j.automatica.2013.01.007","article-title":"State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay","volume":"49","author":"Liu","year":"2013","journal-title":"Automatica"},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0017","doi-asserted-by":"crossref","first-page":"963","DOI":"10.1049\/iet-cta.2013.1163","article-title":"Global output feedback stabilization for a class of stochastic feedforward nonlinear systems with state time delay","volume":"9","author":"Liu","year":"2015","journal-title":"IET Contr. Theory Appl."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108652_bib0018","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1080\/00207179.2013.767942","article-title":"A homogeneous domination approach to state feedback of stochastic high-order feedforward nonlinear systems","volume":"86","author":"Zhao","year":"2013","journal-title":"Int. J. Contr."},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108652_bib0019","first-page":"2106","article-title":"Global output feedback stabilization for a class of upper triangular stochastic nonlinear systems","volume":"87","author":"Zhai","year":"2014","journal-title":"Int. J. Contr."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108652_bib0020","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.automatica.2013.09.044","article-title":"Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay","volume":"50","author":"Zhao","year":"2014","journal-title":"Automatica"},{"issue":"13","key":"10.1016\/j.jfranklin.2026.108652_bib0021","doi-asserted-by":"crossref","first-page":"3909","DOI":"10.1002\/rnc.4112","article-title":"Global stabilization for a class of stochastic nonlinear systems with SISS-like conditions and time delay","volume":"28","author":"Zhang","year":"2018","journal-title":"Int. J. Robust Nonlinear Contr."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108652_bib0022","doi-asserted-by":"crossref","first-page":"3908","DOI":"10.1109\/TSMC.2023.3234177","article-title":"Homogeneous domination approach to global stabilization of stochastic continuous nonlinear time-delay systems with SISS-like conditions","volume":"53","author":"Shao","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108652_bib0023","doi-asserted-by":"crossref","first-page":"4872","DOI":"10.1016\/j.jfranklin.2014.06.012","article-title":"Decentralized global stabilization for stochastic high-order feedforward nonlinear systems with time-varying delays","volume":"351","author":"Jiao","year":"2014","journal-title":"J. Franklin Inst."},{"issue":"16","key":"10.1016\/j.jfranklin.2026.108652_bib0024","doi-asserted-by":"crossref","first-page":"9627","DOI":"10.1016\/j.jfranklin.2018.11.058","article-title":"Observer-based decentralized control of large-scale stochastic high-order feedforward systems with multi time delays","volume":"356","author":"Liu","year":"2019","journal-title":"J. Franklin Inst."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108652_bib0025","doi-asserted-by":"crossref","first-page":"5254","DOI":"10.1109\/TII.2025.3552707","article-title":"Decentralized saturation control for large-scale stochastic systems with strict feedforward structure and its application","volume":"21","author":"Liu","year":"2025","journal-title":"IEEE Trans. Ind. Inf."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108652_bib0026","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1002\/rnc.3868","article-title":"Output feedback stabilization of stochastic feedforward nonlinear time-delay systems with unknown output function","volume":"28","author":"Xie","year":"2018","journal-title":"Int. J. Robust Nonlinear Contr."},{"key":"10.1016\/j.jfranklin.2026.108652_bib0027","doi-asserted-by":"crossref","unstructured":"Q.X. Zhu, H. Wang, Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function, Automatica 87(2018) 166\u2013175.","DOI":"10.1016\/j.automatica.2017.10.004"},{"key":"10.1016\/j.jfranklin.2026.108652_bib0028","doi-asserted-by":"crossref","unstructured":"H.F. Li, X.F. Zhang, M. Li, Design of output feedback controller for stochastic feedforward systems with unknown measurement sensitivity, ISA Trans. 97(2020) 182\u2013188.","DOI":"10.1016\/j.isatra.2019.08.027"},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108652_bib0029","doi-asserted-by":"crossref","first-page":"4408","DOI":"10.1109\/TAC.2019.2954800","article-title":"Logic-based switching control for stabilization of stochastic feedforward nonlinear systems","volume":"65","author":"Yu","year":"2020","journal-title":"IEEE Trans. Automat. Contr."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108652_bib0030","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1080\/07362994.2021.1893749","article-title":"Adaptive output feedback regulation for a class of uncertain feedforward stochastic nonlinear systems","volume":"40","author":"Belfeki","year":"2022","journal-title":"Stoch. Anal. Appl."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108652_bib0031","doi-asserted-by":"crossref","first-page":"2605","DOI":"10.1109\/TAC.2023.3331682","article-title":"Exponential stabilization of stochastic feedforward nonlinear systems: a dynamic gain approach","volume":"69","author":"Cui","year":"2024","journal-title":"IEEE Trans. Automat. Contr."},{"issue":"17","key":"10.1016\/j.jfranklin.2026.108652_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.jfranklin.2024.107288","article-title":"A Lyapunov-Razumikhin control strategy for stochastic nonlinear delayed systems with polynomial conditions","volume":"361","author":"Zhang","year":"2024","journal-title":"J. Franklin Inst."},{"key":"10.1016\/j.jfranklin.2026.108652_bib0033","doi-asserted-by":"crossref","unstructured":"L. Liu, M.R. Kong, A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems, Automatica 151(2023) 110932.","DOI":"10.1016\/j.automatica.2023.110932"},{"key":"10.1016\/j.jfranklin.2026.108652_bib0034","doi-asserted-by":"crossref","unstructured":"L. Liu, R.L. Bai, Output feedback control of stochastic systems in strict-feedforward form with time delays, Automatica 179(2025) 112410.","DOI":"10.1016\/j.automatica.2025.112410"},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108652_bib0035","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1016\/j.automatica.2013.01.054","article-title":"Finite-time stabilization of stochastic nonlinear systems in strict-feedback form","volume":"49","author":"Khoo","year":"2013","journal-title":"Automatica"},{"issue":"11","key":"10.1016\/j.jfranklin.2026.108652_bib0036","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1002\/rnc.3161","article-title":"Continuous finite-time state feedback stabilizers for some nonlinear stochastic systems","volume":"25","author":"Yin","year":"2015","journal-title":"Int. J. Robust Nonlinear Contr."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108652_bib0037","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-024-4118-x","article-title":"New results on finite-time stability and instability theorems for stochastic nonlinear time-varying systems","volume":"68","author":"Zhang","year":"2025","journal-title":"Sci. China Inf. Sci."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108652_bib0038","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/j.isatra.2014.01.005","article-title":"Finite-time stabilization for a class of stochastic nonlinear systems via output feedback","volume":"53","author":"Zha","year":"2014","journal-title":"ISA Trans."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108652_bib0039","doi-asserted-by":"crossref","first-page":"1332","DOI":"10.1080\/00207179.2015.1129439","article-title":"Finite-time state feedback stabilization of stochastic high-order nonlinear feedforward systems","volume":"89","author":"Xie","year":"2016","journal-title":"Int. J. Contr."},{"key":"10.1016\/j.jfranklin.2026.108652_bib0040","doi-asserted-by":"crossref","unstructured":"X.H. Zhang, A.C. Zhang, G.C. Pang, Stochastic finite-time output feedback stabilization of feedforward nonlinear systems, IEEE Access 7(2019) 77083\u201377090.","DOI":"10.1109\/ACCESS.2019.2921801"},{"issue":"10","key":"10.1016\/j.jfranklin.2026.108652_bib0041","doi-asserted-by":"crossref","first-page":"2136","DOI":"10.1002\/rnc.3398","article-title":"Finite-time stabilization of a class of switched stochastic nonlinear systems under arbitrary switching","volume":"26","author":"Huang","year":"2016","journal-title":"Int. J. Robust Nonlinear Contr."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0042","doi-asserted-by":"crossref","first-page":"1960","DOI":"10.1002\/rnc.3994","article-title":"Finite-time stabilization of stochastic low-order nonlinear systems with FT-SISS inverse dynamics","volume":"28","author":"Jiang","year":"2018","journal-title":"Int. J. Robust Nonlinear Contr."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108652_bib0043","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1080\/00207179.2016.1209563","article-title":"Finite-time output feedback control for a class of stochastic low-order nonlinear systems","volume":"90","author":"Liu","year":"2017","journal-title":"Int. J. Contr."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108652_bib0044","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1080\/00207721.2024.2414125","article-title":"Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function","volume":"56","author":"Jiang","year":"2025","journal-title":"Int. J. Syst. Sci."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0045","doi-asserted-by":"crossref","first-page":"2386","DOI":"10.1002\/rnc.4882","article-title":"Finite-time stabilization for a class of stochastic low-order nonlinear systems with unknown control coefficients","volume":"30","author":"Shao","year":"2020","journal-title":"Int. J. Robust Nonlinear Contr."},{"key":"10.1016\/j.jfranklin.2026.108652_bib0046","doi-asserted-by":"crossref","unstructured":"L. Liu, G. Sun, Finite-time output feedback control of stochastic low-order feedforward nonlinear systems, Asian J. Contr. (2025). 10.1002\/asjc.3796.","DOI":"10.1002\/asjc.3796"},{"key":"10.1016\/j.jfranklin.2026.108652_bib0047","doi-asserted-by":"crossref","first-page":"1329","DOI":"10.1007\/s11071-022-07882-w","article-title":"Event-triggered finite-time adaptive trajectory tracking control for a class of nonlinear non-strict-feedback systems with input saturation and application to a single-link robot","volume":"111","author":"Jiang","year":"2023","journal-title":"Nonlinear Dyn."},{"issue":"12","key":"10.1016\/j.jfranklin.2026.108652_bib0048","doi-asserted-by":"crossref","first-page":"7839","DOI":"10.1109\/TCYB.2024.3457769","article-title":"Neuroadaptive output-feedback tracking control for stochastic nonlower triangular nonlinear systems with dead-zone input","volume":"54","author":"Feng","year":"2024","journal-title":"IEEE Trans. Cybern."},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108652_bib0049","doi-asserted-by":"crossref","first-page":"3815","DOI":"10.1109\/TFUZZ.2024.3384588","article-title":"Fuzzy adaptive control for stochastic nonstrict feedback systems with multiple time-delays: a novel Lyapunov-Krasovskii method","volume":"32","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Fuzzy Syst."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108652_bib0050","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TAC.2025.3595002","article-title":"Distributed finite-time bipartite consensus control for constrained nonlinear MASs: a switched function approach based on prioritized strategy","volume":"71","author":"Li","year":"2026","journal-title":"IEEE Trans. Automat. Contr."}],"container-title":["Journal of the Franklin Institute"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226002528?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226002528?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T01:14:55Z","timestamp":1778894095000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0016003226002528"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":50,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2026,5]]}},"alternative-id":["S0016003226002528"],"URL":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108652","relation":{},"ISSN":["0016-0032"],"issn-type":[{"value":"0016-0032","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Finite-time stabilization of low-order stochastic feedforward systems with general power structure via output feedback control","name":"articletitle","label":"Article Title"},{"value":"Journal of the Franklin Institute","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108652","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Franklin Institute. Published by Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108652"}}