{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T03:02:28Z","timestamp":1790650948371,"version":"4.1.0"},"reference-count":31,"publisher":"Elsevier BV","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\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62403150"],"award-info":[{"award-number":["62403150"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62273111"],"award-info":[{"award-number":["62273111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["ISA Transactions"],"published-print":{"date-parts":[[2026,5]]},"DOI":"10.1016\/j.isatra.2026.03.015","type":"journal-article","created":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T16:04:06Z","timestamp":1773158646000},"page":"211-220","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["Geometric insight into linear augmented observers for uncertain systems"],"prefix":"10.1016","volume":"172","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1534-4087","authenticated-orcid":false,"given":"Junhui","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beili","family":"Gong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.isatra.2026.03.015_bib0005","doi-asserted-by":"crossref","first-page":"3273","DOI":"10.1109\/TIE.2016.2583412","article-title":"Disturbance\/uncertainty estimation and attenuation techniques in PMSM drives\u2013a survey","volume":"64","author":"Yang","year":"2017","journal-title":"IEEE Trans Ind Electron"},{"key":"10.1016\/j.isatra.2026.03.015_bib0010","doi-asserted-by":"crossref","DOI":"10.1016\/j.conengprac.2022.105158","article-title":"Disturbance observers and extended state observers for marine vehicles: a survey","volume":"123","author":"Gu","year":"2022","journal-title":"Control Eng Pract"},{"issue":"3","key":"10.1016\/j.isatra.2026.03.015_bib0015","doi-asserted-by":"crossref","first-page":"2042","DOI":"10.1109\/TIE.2019.2903752","article-title":"Disturbance observer-based robust control and its applications: 35th anniversary overview","volume":"67","author":"Sariyildiz","year":"2020","journal-title":"IEEE Trans Ind Electron"},{"key":"10.1016\/j.isatra.2026.03.015_bib0020","doi-asserted-by":"crossref","DOI":"10.1016\/j.arcontrol.2025.101044","article-title":"Advanced feedforward control techniques: comprehensive review and a real-time industrial application","volume":"61","author":"Nguyen-Khac","year":"2026","journal-title":"Annu Rev Control"},{"key":"10.1016\/j.isatra.2026.03.015_bib0025","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1016\/j.isatra.2020.02.029","article-title":"An adaptive sliding mode observer for inverted pendulum under mass variation and disturbances with experimental validation","volume":"102","author":"Jmel","year":"2020","journal-title":"ISA Trans"},{"issue":"2","key":"10.1016\/j.isatra.2026.03.015_bib0030","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1109\/TIE.2015.2478397","article-title":"Disturbance-observer-based control and related methods\u2013an overview","volume":"63","author":"Chen","year":"2016","journal-title":"IEEE Trans Ind Electron"},{"key":"10.1016\/j.isatra.2026.03.015_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.ejcon.2022.100630","article-title":"Performance, robustness and noise amplification trade-offs in disturbance observer control design","volume":"65","author":"Tena","year":"2022","journal-title":"Eur J Control"},{"issue":"9","key":"10.1016\/j.isatra.2026.03.015_bib0040","doi-asserted-by":"crossref","first-page":"1571","DOI":"10.1080\/00207729508929120","article-title":"State estimation of dynamical systems with nonlinearities by using proportional-integral observer","volume":"26","author":"S\u00f6ffker","year":"1995","journal-title":"Int J Syst Sci"},{"issue":"3","key":"10.1016\/j.isatra.2026.03.015_bib0045","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1109\/TIE.2008.2011621","article-title":"From PID to active disturbance rejection control","volume":"56","author":"Han","year":"2009","journal-title":"IEEE Trans Ind Electron"},{"key":"10.1016\/j.isatra.2026.03.015_bib0050","series-title":"Proceedings of the 2003 American Control Conference","first-page":"4989","article-title":"Scaling and bandwidth-parameterization based controller tuning","volume":"vol. 6","author":"Gao","year":"2003"},{"issue":"12","key":"10.1016\/j.isatra.2026.03.015_bib0055","doi-asserted-by":"crossref","first-page":"4792","DOI":"10.1109\/TIE.2011.2182011","article-title":"Generalized extended state observer based control for systems with mismatched uncertainties","volume":"59","author":"Li","year":"2012","journal-title":"IEEE Trans Ind Electron"},{"key":"10.1016\/j.isatra.2026.03.015_bib0060","series-title":"Proportional-integral observer in robust control, fault detection, and decentralized control of dynamic systems","first-page":"13","author":"Shafai","year":"2015"},{"issue":"10","key":"10.1016\/j.isatra.2026.03.015_bib0065","doi-asserted-by":"crossref","first-page":"2960","DOI":"10.1002\/rnc.4531","article-title":"Observers and observability for uncertain nonlinear systems: a necessary and sufficient condition","volume":"29","author":"Bai","year":"2019","journal-title":"Int J Robust Nonlinear Control"},{"key":"10.1016\/j.isatra.2026.03.015_bib0070","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.isatra.2021.11.023","article-title":"Performance analysis of typical linear augmented observers for a class of MIMO systems with nonlinear uncertainty","volume":"128","author":"Chen","year":"2022","journal-title":"ISA Trans"},{"issue":"2","key":"10.1016\/j.isatra.2026.03.015_bib0075","doi-asserted-by":"crossref","DOI":"10.1007\/s11432-018-9644-3","article-title":"On the conceptualization of total disturbance and its profound implications","volume":"63","author":"Chen","year":"2019","journal-title":"Sci China Inf Sci"},{"key":"10.1016\/j.isatra.2026.03.015_bib0080","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.isatra.2022.06.032","article-title":"On the equivalence between generalized proportional integral observer and disturbance observer","volume":"133","author":"Rojas","year":"2023","journal-title":"ISA Trans"},{"key":"10.1016\/j.isatra.2026.03.015_bib0085","doi-asserted-by":"crossref","first-page":"590","DOI":"10.1016\/j.isatra.2022.11.012","article-title":"On convergence of extended state observers for nonlinear systems with non-differentiable uncertainties","volume":"136","author":"Wu","year":"2023","journal-title":"ISA Trans"},{"key":"10.1016\/j.isatra.2026.03.015_bib0090","doi-asserted-by":"crossref","DOI":"10.1016\/j.sysconle.2021.104897","article-title":"Generalized observability analysis and observer design for a class of systems with multiple uncertain dynamics and measurement biases","volume":"150","author":"Zhang","year":"2021","journal-title":"Syst Control Lett"},{"key":"10.1016\/j.isatra.2026.03.015_bib0095","series-title":"Controlled and Conditioned Invariants in Linear System Theory","author":"Basile","year":"1992"},{"key":"10.1016\/j.isatra.2026.03.015_bib0100","series-title":"Control Theory for Linear Systems","author":"Trentelman","year":"2001"},{"key":"10.1016\/j.isatra.2026.03.015_bib0105","doi-asserted-by":"crossref","DOI":"10.1016\/j.arcontrol.2023.100928","article-title":"Revisiting disturbance decoupling with an optimization perspective","volume":"57","author":"Sars\u0131lmaz","year":"2024","journal-title":"Annu Rev Control"},{"key":"10.1016\/j.isatra.2026.03.015_bib0110","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2021.109572","article-title":"A structural approach to unknown inputs observation for switching linear systems","volume":"129","author":"Conte","year":"2021","journal-title":"Automatica"},{"issue":"1","key":"10.1016\/j.isatra.2026.03.015_bib0115","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s11768-023-00130-5","article-title":"On geometric interpretation of extended state observer: a preliminary study","volume":"21","author":"Chen","year":"2023","journal-title":"Control Theory Technol"},{"issue":"4","key":"10.1016\/j.isatra.2026.03.015_bib0120","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1109\/JAS.2022.105929","article-title":"Generalized-extended-state-observer and equivalent-input-disturbance methods for active disturbance rejection: deep observation and comparison","volume":"10","author":"She","year":"2023","journal-title":"IEEE\/CAA J Autom Sinica"},{"key":"10.1016\/j.isatra.2026.03.015_bib0125","series-title":"Linear Systems","author":"Antsaklis","year":"2006"},{"key":"10.1016\/j.isatra.2026.03.015_bib0130","series-title":"Introduction to Stochastic Control Theory","author":"\u00c5str\u00f6m","year":"2006"},{"issue":"5","key":"10.1016\/j.isatra.2026.03.015_bib0135","doi-asserted-by":"crossref","first-page":"814","DOI":"10.1109\/TAC.2006.875019","article-title":"Applying discrete-time proportional integral observers for state and disturbance estimations","volume":"51","author":"Chang","year":"2006","journal-title":"IEEE Trans Autom Control"},{"key":"10.1016\/j.isatra.2026.03.015_bib0140","series-title":"Contraction Theory for Dynamical Systems","author":"Bullo","year":"2024"},{"issue":"5","key":"10.1016\/j.isatra.2026.03.015_bib0145","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1109\/TCT.1972.1083507","article-title":"The measure of a matrix as a tool to analyze computer algorithms for circuit analysis","volume":"19","author":"Desoer","year":"1972","journal-title":"IEEE Trans Circ Theory"},{"key":"10.1016\/j.isatra.2026.03.015_bib0150","series-title":"Nonlinear Systems","author":"Khalil","year":"2001"},{"key":"10.1016\/j.isatra.2026.03.015_bib0155","series-title":"Introduction to Smooth Manifolds","author":"Lee","year":"2012"}],"container-title":["ISA Transactions"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019057826001345?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019057826001345?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T17:39:47Z","timestamp":1776188387000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0019057826001345"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5]]},"references-count":31,"alternative-id":["S0019057826001345"],"URL":"https:\/\/doi.org\/10.1016\/j.isatra.2026.03.015","relation":{},"ISSN":["0019-0578"],"issn-type":[{"value":"0019-0578","type":"print"}],"subject":[],"published":{"date-parts":[[2026,5]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Geometric insight into linear augmented observers for uncertain systems","name":"articletitle","label":"Article Title"},{"value":"ISA Transactions","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.isatra.2026.03.015","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 International Society of Automation. Published by Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}]}}