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The capability of the descriptor model to show the real model is more reasonable than the standard state-space model. Based on the constructed Lyapunov function method and applying the bilinear matrix inequalities technique, all of the constraints are handled by introducing the new theorem. This theorem aims to design a state feedback with the intent that the closed-loop system be admissible. Here, the results are less conservative than other approaches. This issue has not yet been fully addressed in the literature, especially on AUVs. Theorem achievement is implemented on new AUV descriptor model that is obtained and introduced here. This method covers both neutral and descriptor systems. Also, it can be generalized and applied to conventional AUVs or similar dynamics. Examples and simulation results illustrate the effectiveness of the proposed approach.<\/jats:p>","DOI":"10.1177\/01423312211037819","type":"journal-article","created":{"date-parts":[[2021,8,28]],"date-time":"2021-08-28T14:27:18Z","timestamp":1630160838000},"page":"484-496","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Stabilizer design for an under-actuated autonomous underwater vehicle in a descriptor model under unknown time delay and uncertainty"],"prefix":"10.1177","volume":"44","author":[{"given":"Mohammad","family":"Hedayati Khodayari","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Ferdowsi University of Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6689-9176","authenticated-orcid":false,"given":"Naser","family":"Pariz","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Ferdowsi University of Mashhad, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3137-9167","authenticated-orcid":false,"given":"Saeed","family":"Balochian","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Gonabad branch, Islamic Azad University, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2021,8,28]]},"reference":[{"key":"bibr1-01423312211037819","author":"Binazadeh T","year":"2018","journal-title":"Lipschitz nonlinear systems with time-delay"},{"issue":"2","key":"bibr2-01423312211037819","volume":"49","author":"Cao YY","year":"2002","journal-title":"IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications"},{"key":"bibr3-01423312211037819","unstructured":"Caverly RJ, Forbes JR (2019) LMI properties and applications in systems, stability, and control theory, Cornell University. 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