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The original zeroing neural network (OZNN) can work well to handle DSE under a noise-free environment, but may not work in noise. Though an integral-enhanced zeroing neural network (IEZNN) can be employed to solve the DSE under multiple-noise, it may fall flat under linear noise, and its convergence speed is unsatisfactory. Therefore, an accelerated double-integral zeroing neural network (ADIZNN) is proposed based on an innovative design formula to resist linear noise and accelerate convergence. Besides, theoretical proofs verify the convergence and robustness of the ADIZNN model. Moreover, simulation experiments indicate that the convergence rate and anti-noise ability of the ADIZNN are far superior to the OZNN and IEZNN under linear noise. Finally, chaos control of the sine function memristor (SFM) chaotic system is provided to suggest that the controller based on the ADIZNN has a smaller amount of error and higher accuracy than other ZNNs.<\/jats:p>","DOI":"10.3390\/axioms12030287","type":"journal-article","created":{"date-parts":[[2023,3,9]],"date-time":"2023-03-09T02:33:16Z","timestamp":1678329196000},"page":"287","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An Accelerated Double-Integral ZNN with Resisting Linear Noise for Dynamic Sylvester Equation Solving and Its Application to the Control of the SFM Chaotic System"],"prefix":"10.3390","volume":"12","author":[{"given":"Luyang","family":"Han","sequence":"first","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongjun","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9036-2723","authenticated-orcid":false,"given":"Bolin","family":"Liao","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheng","family":"Hua","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1109\/LSP.2016.2608858","article-title":"R-FUSE: Robust fast fusion of multiband images based on solving a Sylvester equation","volume":"23","author":"Wei","year":"2016","journal-title":"IEEE Signal Process. 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