{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T02:16:11Z","timestamp":1766974571318,"version":"3.48.0"},"reference-count":31,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T00:00:00Z","timestamp":1765756800000},"content-version":"vor","delay-in-days":14,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB3001604"],"award-info":[{"award-number":["2023YFB3001604"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971413"],"award-info":[{"award-number":["11971413"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>This paper establishes several equivalent conditions for a unique positive definite solution of the unified algebraic Lyapunov matrix equation (UALE). Then, two iterative algorithms for the UALE driven by error precision are proposed, which can be accelerated by optimizing the calculation of series terms. The algorithm's convergence, computational complexity, and optimal parameter selection are discussed, supported by a series of numerical experiments that illustrate the effectiveness and superiority of our results. Finally, by constructing a positive semi\u2010definite matrix and employing matrix\u2010singular inequality, a new robust bound for the unified perturbed system is derived, generalizing some of the existing results. Some numerical experiments demonstrate its practicality and advantage.<\/jats:p>","DOI":"10.1002\/nla.70055","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T23:10:50Z","timestamp":1765840250000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Accelerated Algorithms for Solving the Unified Algebraic Lyapunov Matrix Equation and Its Application in Stability of Perturbed Systems"],"prefix":"10.1002","volume":"32","author":[{"given":"Yan","family":"Xu","sequence":"first","affiliation":[{"name":"School of Mathematics and Computational Science &amp; Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University  Xiangtan People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1056-0274","authenticated-orcid":false,"given":"Jianzhou","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science &amp; Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University  Xiangtan People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-0526-6818","authenticated-orcid":false,"given":"Ze","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computational Science &amp; Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan University  Xiangtan People's Republic of China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,12,15]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2017.2711538"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.2514\/1.G000036"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2021.09.013"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijhydene.2022.06.207"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/JESTPE.2021.3063228"},{"volume-title":"Digital Control and Estimation: A Unified Approach","year":"2004","author":"Middleton R. 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