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This study proposes an MRAC design method that takes states from the model using only the input and output measured values of the controlled plant when the derivatives of various orders of the controlled plant are not measurable. By adopting the method of taking states from the model, this paper not only solves the problem of the plant\u2019s states being unmeasurable but also significantly enhances the system\u2019s disturbance rejection capability. The effectiveness of the method was verified through digital simulations, showing that the controlled plant output can better follow the reference model output, indicating that this approach has greater application value.<\/jats:p>","DOI":"10.1177\/14727978251321464","type":"journal-article","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:16:56Z","timestamp":1740143816000},"page":"3443-3452","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["A new design method for model reference adaptive control systems based on Lyapunov stability theory"],"prefix":"10.66113","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-8406-3136","authenticated-orcid":false,"given":"Zixuan","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mechanical and Electrical Engineering, Beijing Institute of Graphic Communication, Beijing, China"}]},{"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[{"name":"Division of On-line Testing and General Measurement Technology, Shanghai Institute of Measurement and Testing Technology, Shanghai, China"}]},{"given":"Yi","family":"Zhang","sequence":"additional","affiliation":[{"name":"Division of On-line Testing and General Measurement Technology, Shanghai Institute of Measurement and Testing Technology, Shanghai, China"}]},{"given":"Xiaojing","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electrical Engineering, Beijing Institute of Graphic Communication, Beijing, China"}]},{"given":"Yongdong","family":"Wei","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electrical Engineering, Beijing Institute of Graphic Communication, Beijing, China"}]},{"given":"Wen","family":"Fang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electrical Engineering, Beijing Institute of Graphic Communication, Beijing, China"}]}],"member":"55691","published-online":{"date-parts":[[2025,2,21]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/AMM.602-605.1367"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2022.07.011"},{"issue":"03","key":"e_1_3_3_4_2","first-page":"490","article-title":"Integral model reference adaptive control with bounded switching gains for space inertial sensor output regulation","volume":"54","author":"Sun X","year":"2024","unstructured":"Sun X, Wu S, Shen Q. 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