{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:03Z","timestamp":1760148363620,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T00:00:00Z","timestamp":1682467200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province","award":["ZR2021MF012","2021GXRC100"],"award-info":[{"award-number":["ZR2021MF012","2021GXRC100"]}]},{"name":"Colleges and Universities Twenty Terms Foundation of Jinan City","award":["ZR2021MF012","2021GXRC100"],"award-info":[{"award-number":["ZR2021MF012","2021GXRC100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates the stabilization of nonlinear systems with external disturbances, which are both bounded and unbounded. Firstly, the stabilization problem of the nominal nonlinear system is realized, and the corresponding stabilization controllers are designed. Then, three suitable filters are proposed and applied to asymptotically estimate the corresponding disturbances, and the disturbance estimators are presented and used to exactly eliminate the corresponding disturbances. Then, the disturbance estimator (DE)-based controllers are proposed to stabilize such nonlinear systems. It should be pointed out the unbounded disturbances are exactly estimated by suitable filters, which has advantages over the existing results. Finally, two illustrative examples, which have certain symmetrical properties, are taken, and the related numerical simulations are carried out to verify the effectiveness and correctness of the proposed results.<\/jats:p>","DOI":"10.3390\/sym15050987","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T04:30:47Z","timestamp":1682569847000},"page":"987","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Stabilization of Nonlinear Systems with External Disturbances Using the DE-Based Control Method"],"prefix":"10.3390","volume":"15","author":[{"given":"Keran","family":"Sun","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8836-0964","authenticated-orcid":false,"given":"Rongwei","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"103789","DOI":"10.1016\/j.bspc.2022.103789","article-title":"A hybrid swarming computing approach to solve the biological nonlinear Leptospirosis system","volume":"77","author":"Botmart","year":"2022","journal-title":"Biomed. 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