{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T15:54:45Z","timestamp":1783958085365,"version":"3.55.0"},"reference-count":27,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100004826","name":"Beijing Natural Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005089","name":"Natural Science Foundation of Beijing Municipality","doi-asserted-by":"publisher","award":["4244089"],"award-info":[{"award-number":["4244089"]}],"id":[{"id":"10.13039\/501100005089","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62373066"],"award-info":[{"award-number":["62373066"]}],"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":[[2025,1]]},"DOI":"10.1016\/j.isatra.2024.10.029","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T11:19:35Z","timestamp":1731410375000},"page":"446-456","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["Fault diagnosis and tolerant strategy for MIMO system based on\n                    <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" altimg=\"si8.svg\" display=\"inline\" id=\"d1e1128\">\n                      <mml:mi>\u03bd<\/mml:mi>\n                    <\/mml:math>\n                    -gap metric"],"prefix":"10.1016","volume":"156","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3316-914X","authenticated-orcid":false,"given":"Shufeng","family":"Zhang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changan","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuntao","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiang","family":"Yin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.isatra.2024.10.029_b1","article-title":"Flatness-based algebraic fault diagnosis for distributed-parameter systems","volume":"117","author":"Fischer","year":"2022","journal-title":"Automatica"},{"key":"10.1016\/j.isatra.2024.10.029_b2","first-page":"1","article-title":"Sparse Wasserstein stationary subspace analysis for fault detection and diagnosis of nonstationary industrial processes","author":"Huang","year":"2024","journal-title":"ISA Trans"},{"key":"10.1016\/j.isatra.2024.10.029_b3","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.isatra.2020.06.016","article-title":"Super-twisting control using higher order disturbance observer for control of SISO and MIMO coupled systems","volume":"106","author":"Sadala","year":"2020","journal-title":"ISA Trans"},{"key":"10.1016\/j.isatra.2024.10.029_b4","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.isatra.2023.12.019","article-title":"Cross-domain fault diagnosis method for rolling bearings based on contrastive universal domain adaptation","volume":"146","author":"Kang","year":"2024","journal-title":"ISA Trans"},{"issue":"10","key":"10.1016\/j.isatra.2024.10.029_b5","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.1109\/9.956059","article-title":"A new controller architecture for high performance, robust, and fault-tolerant control","volume":"46","author":"Zhou","year":"2001","journal-title":"IEEE Trans Autom Control"},{"key":"10.1016\/j.isatra.2024.10.029_b6","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.automatica.2018.10.047","article-title":"Performance-based fault detection and fault-tolerant control for automatic control systems","volume":"99","author":"Li","year":"2019","journal-title":"Automatica"},{"key":"10.1016\/j.isatra.2024.10.029_b7","series-title":"Advanced methods for fault diagnosis and fault-tolerant control","author":"Ding","year":"2020"},{"key":"10.1016\/j.isatra.2024.10.029_b8","doi-asserted-by":"crossref","unstructured":"Ding SX. Application of factorization and gap metric techniques to fault detection and isolation part I: A factorization technique based FDI framework. In: Proc. IFAC symp. safeprocess. Paris, France; 2015, p. 113\u20138.","DOI":"10.1016\/j.ifacol.2015.09.513"},{"key":"10.1016\/j.isatra.2024.10.029_b9","doi-asserted-by":"crossref","unstructured":"Ding SX. Application of factorization and gap metric techniques to fault detection and isolation part II: Gap metric technique aided FDI performance analysis. In: Proc. IFAC symp. safeprocess. Paris, France; 2015, p. 119\u201324.","DOI":"10.1016\/j.ifacol.2015.09.514"},{"issue":"17","key":"10.1016\/j.isatra.2024.10.029_b10","doi-asserted-by":"crossref","first-page":"2928","DOI":"10.1002\/rnc.3033","article-title":"Model falsification using set-valued observers for a class of discrete-time dynamic systems: A coprime factorization approach","volume":"24","author":"Rosa","year":"2014","journal-title":"Internat J Robust Nonlinear Control"},{"issue":"2","key":"10.1016\/j.isatra.2024.10.029_b11","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/TSMC.2017.2759144","article-title":"Fault-tolerant control for systems with model uncertainty and multiplicative faults","volume":"50","author":"Zhao","year":"2020","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"issue":"12","key":"10.1016\/j.isatra.2024.10.029_b12","doi-asserted-by":"crossref","first-page":"12687","DOI":"10.1109\/TCYB.2021.3086193","article-title":"An integrated model-based and data-driven gap metric method for fault detection and isolation","volume":"52","author":"Jin","year":"2022","journal-title":"IEEE Trans Cybern"},{"issue":"3","key":"10.1016\/j.isatra.2024.10.029_b13","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1109\/TAC.2017.2735023","article-title":"A data-driven computation method for the gap metric and the optimal stability margin","volume":"63","author":"Koenings","year":"2018","journal-title":"IEEE Trans Autom Control"},{"issue":"9","key":"10.1016\/j.isatra.2024.10.029_b14","doi-asserted-by":"crossref","first-page":"5715","DOI":"10.1109\/TSMC.2023.3276060","article-title":"Small fault diagnosis with gap metric","volume":"53","author":"Jin","year":"2023","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"issue":"8","key":"10.1016\/j.isatra.2024.10.029_b15","doi-asserted-by":"crossref","first-page":"7765","DOI":"10.1109\/TCYB.2021.3051368","article-title":"Fault detection for systems with model uncertainty and disturbance via coprime factorization and gap metric","volume":"52","author":"Wang","year":"2022","journal-title":"IEEE Trans Cybern"},{"key":"10.1016\/j.isatra.2024.10.029_b16","doi-asserted-by":"crossref","DOI":"10.1016\/j.automatica.2020.109029","article-title":"Gap metric techniques and their application to fault detection performance analysis and fault isolation schemes","volume":"118","author":"Li","year":"2020","journal-title":"Automatica"},{"issue":"2","key":"10.1016\/j.isatra.2024.10.029_b17","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1109\/TCST.2009.2018451","article-title":"Feedback control structures, embedded residual signals, and feedback control schemes with an integrated residual access","volume":"18","author":"Ding","year":"2010","journal-title":"IEEE Trans Control Syst Technol"},{"issue":"10","key":"10.1016\/j.isatra.2024.10.029_b18","doi-asserted-by":"crossref","first-page":"2615","DOI":"10.1016\/j.automatica.2014.08.022","article-title":"Data-driven realizations of kernel and image representations and their application to fault detection and control system design","volume":"50","author":"Ding","year":"2014","journal-title":"Automatica"},{"issue":"4","key":"10.1016\/j.isatra.2024.10.029_b19","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1109\/TSMC.2015.2450203","article-title":"Optimal design of residual-driven dynamic compensator using iterative algorithms with guaranteed convergence","volume":"46","author":"Zhang","year":"2016","journal-title":"IEEE Trans Syst Man Cybern: Syst"},{"key":"10.1016\/j.isatra.2024.10.029_b20","series-title":"Model-based fault diagnosis technics: Design schemes, algorithms and tools","author":"Ding","year":"2013"},{"key":"10.1016\/j.isatra.2024.10.029_b21","series-title":"Uncertainty and feedback: H\u221e loop-shaping and the \u03bd-gap metric","author":"Vinnicombe","year":"2000"},{"issue":"8","key":"10.1016\/j.isatra.2024.10.029_b22","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.automatica.2011.02.049","article-title":"Parameterization and identification of multivariable state-space systems: A canonical approach","volume":"47","author":"Mercere","year":"2011","journal-title":"Automatica"},{"key":"10.1016\/j.isatra.2024.10.029_b23","series-title":"Essentials of robust control","author":"Zhou","year":"1998"},{"issue":"12","key":"10.1016\/j.isatra.2024.10.029_b24","first-page":"902","article-title":"Finite-horizon H\u221e fault estimation for uncertain linear discrete time-varying systems with known inputs","volume":"60","author":"Shen","year":"2013","journal-title":"IEEE Trans Circuits Syst II: Express Briefs"},{"issue":"8","key":"10.1016\/j.isatra.2024.10.029_b25","doi-asserted-by":"crossref","first-page":"3817","DOI":"10.1002\/cta.3895","article-title":"Observer-based residual-driven dynamic compensation strategy for performance improvement of grid-forming inverter","volume":"52","author":"Zhang","year":"2024","journal-title":"Int J Circuit Theory Appl"},{"key":"10.1016\/j.isatra.2024.10.029_b26","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1016\/j.isatra.2024.02.012","article-title":"Disturbance rejection of offshore drilling platforms: An equivalent-input-disturbance-based dynamic positioning control method","volume":"147","author":"Ma","year":"2024","journal-title":"ISA Trans"},{"issue":"8","key":"10.1016\/j.isatra.2024.10.029_b27","doi-asserted-by":"crossref","first-page":"8146","DOI":"10.1109\/TIE.2021.3104602","article-title":"A residual-generator-based plug-and-play control scheme toward enhancing power quality in AC microgrids","volume":"69","author":"Luo","year":"2022","journal-title":"IEEE Trans Ind Electron"}],"container-title":["ISA Transactions"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019057824005068?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0019057824005068?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T20:23:01Z","timestamp":1777407781000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0019057824005068"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":27,"alternative-id":["S0019057824005068"],"URL":"https:\/\/doi.org\/10.1016\/j.isatra.2024.10.029","relation":{},"ISSN":["0019-0578"],"issn-type":[{"value":"0019-0578","type":"print"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Fault diagnosis and tolerant strategy for MIMO system based on -gap metric","name":"articletitle","label":"Article Title"},{"value":"ISA Transactions","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.isatra.2024.10.029","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 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"}]}}