{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:12Z","timestamp":1740103692761,"version":"3.37.3"},"reference-count":26,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T00:00:00Z","timestamp":1589241600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61673247","JQ201719"],"award-info":[{"award-number":["61673247","JQ201719"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Research Fund for Distinguished Young Scholars and Excellent Young Scholars of Shandong Province","award":["61673247","JQ201719"],"award-info":[{"award-number":["61673247","JQ201719"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,5,12]]},"abstract":"<jats:p>Based on the classical finite-time stability theory, the problem of finite-time stability (<jats:italic>FTS<\/jats:italic>) for time-varying nonlinear systems is investigated in this paper. Several <jats:italic>FTS<\/jats:italic> theorems involving global form and local form are presented, and an estimate of the settling-time of such systems is obtained. As an application, we consider the problem of asymptotic stabilization of the Brockett integrator subject to time-varying disturbance. By the switched finite-time controller design methodology, we establish a sufficient condition to guarantee the relative asymptotic stability. For Brockett-like integrator subject to time-varying disturbance, we achieve better convergence performance. Examples and their simulations are given to demonstrate the applicability of the proposed results.<\/jats:p>","DOI":"10.1155\/2020\/8704505","type":"journal-article","created":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T23:31:31Z","timestamp":1589326291000},"page":"1-7","source":"Crossref","is-referenced-by-count":6,"title":["Finite-Time Stability for a Class of Underactuated Systems Subject to Time-Varying Disturbance"],"prefix":"10.1155","volume":"2020","author":[{"given":"Jie","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Ji\u2019nan 250014, China"}]},{"given":"Dan","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Ji\u2019nan 250014, China"}]},{"given":"Xinyi","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Ji\u2019nan 250014, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5124-7159","authenticated-orcid":true,"given":"Xiaodi","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Ji\u2019nan 250014, China"},{"name":"Center for Control and Engineering Computation, Shandong Normal University, Ji\u2019nan 250014, China"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.12.030"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.10.090"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2015.10.002"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2017.12.022"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.08.003"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/9878369"},{"issue":"8","key":"7","first-page":"1840","volume":"28","year":"2016","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/0324047"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1137\/s0363012997321358"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1109\/9.668834"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s11431-016-9054-y"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.11.046"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2007.12.002"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/tac.2011.2179869"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.15388\/na.2018.6.6"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1080\/00207170701650303"},{"year":"2014","key":"18"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2016.06.004"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2018069"},{"issue":"1","key":"21","first-page":"181","volume":"27","year":"1983","journal-title":"Differential Geometric Control Theory"},{"year":"2006","key":"23"},{"issue":"8","key":"24","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1016\/j.na.2005.03.086","volume":"62","year":"2005","journal-title":"Nonlinear Analysis-Theory Methods & Applications"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1080\/02286203.2006.11442374"},{"issue":"12","key":"26","doi-asserted-by":"crossref","first-page":"1976","DOI":"10.1049\/iet-cta.2016.1290","volume":"11","year":"2017","journal-title":"IET Control Theory & Applications"},{"year":"1966","key":"27"},{"year":"2007","key":"28"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8704505.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8704505.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/8704505.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,12]],"date-time":"2020-05-12T23:31:36Z","timestamp":1589326296000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/8704505\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,12]]},"references-count":26,"alternative-id":["8704505","8704505"],"URL":"https:\/\/doi.org\/10.1155\/2020\/8704505","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,5,12]]}}}