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The proposed intermediate observer involves the integral term to improve the estimation accuracy, and the matching condition of the observer is not required. Based on the estimation of system states and faults, a decentralized fault-tolerant control strategy is proposed to stabilize the interconnected system in the presence of faults. The cyclic-small-gain method is used to handle unknown interconnections, ensuring that the resulting closed-loop system achieves bounded stability. By constructing appropriate Lyapunov function candidates, the bounded stability constraints of the closed-loop system are formulated in the form of Linear Matrix Inequalities (LMIs), the observer and controller gain matrices are obtained simultaneously. Two examples are provided at the end of the article to validate our method.<\/jats:p>","DOI":"10.1177\/09596518251341547","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T13:23:28Z","timestamp":1753277008000},"page":"1665-1675","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Fault-tolerant control of interconnected systems with unknown interconnections based on proportional-integral intermediate observers"],"prefix":"10.1177","volume":"239","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8827-2064","authenticated-orcid":false,"given":"Liwei","family":"Li","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing, P.R. 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