{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T04:32:17Z","timestamp":1728534737633},"reference-count":33,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2018,7,23]],"date-time":"2018-07-23T00:00:00Z","timestamp":1532304000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2019,4]]},"abstract":" Based on proximal subdifferentials and subgradients, and instrumented with an extended Caputo differintegral operator, the stability analysis of a general class of fractional-order nonlinear systems is considered by means of non-smooth but convex Lyapunov functions. This facilitates concluding the Mittag\u2013Leffler stability for fractional-order systems whose solutions are not necessarily differentiable in any integer-order sense. As a solution to the problem of robust command of fractional-order systems subject to unknown but Lebesgue-measurable and bounded disturbances, a unit-vector-like integral sliding mode controller is proposed. Numerical simulations are conducted to highlight the reliability of the proposed method in the analysis and design of fractional-order systems closed by non-smooth robust controllers. <\/jats:p>","DOI":"10.1177\/0142331218785694","type":"journal-article","created":{"date-parts":[[2018,7,23]],"date-time":"2018-07-23T13:00:52Z","timestamp":1532350852000},"page":"1627-1639","update-policy":"http:\/\/dx.doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":14,"title":["Non-smooth convex Lyapunov functions for stability analysis of fractional-order systems"],"prefix":"10.1177","volume":"41","author":[{"ORCID":"http:\/\/orcid.org\/0000-0001-5125-2644","authenticated-orcid":false,"given":"Aldo-Jonathan","family":"Mu\u00f1oz-V\u00e1zquez","sequence":"first","affiliation":[{"name":"Mechatronic Engineering, Polytechnic University of Victoria, Ciudad Victoria, Tamaulipas, Mexico"}]},{"given":"Vicente","family":"Parra-Vega","sequence":"additional","affiliation":[{"name":"Robotics and Advanced Manufacturing, Research Center for Advanced Studies, Saltillo, Coahuila, Mexico"}]},{"given":"Anand","family":"S\u00e1nchez-Orta","sequence":"additional","affiliation":[{"name":"Robotics and Advanced Manufacturing, Research Center for Advanced Studies, Saltillo, Coahuila, Mexico"}]}],"member":"179","published-online":{"date-parts":[[2018,7,23]]},"reference":[{"doi-asserted-by":"publisher","key":"bibr1-0142331218785694","DOI":"10.1016\/j.cnsns.2014.01.022"},{"doi-asserted-by":"publisher","key":"bibr2-0142331218785694","DOI":"10.1134\/S0012266110050058"},{"volume-title":"Differential Inclusions: Set-Valued Maps and Viability Theory","year":"2012","author":"Aubin J","key":"bibr3-0142331218785694"},{"doi-asserted-by":"publisher","key":"bibr4-0142331218785694","DOI":"10.1016\/j.sigpro.2006.02.022"},{"doi-asserted-by":"publisher","key":"bibr5-0142331218785694","DOI":"10.1049\/iet-cta.2016.0950"},{"doi-asserted-by":"publisher","key":"bibr6-0142331218785694","DOI":"10.1177\/0142331216634427"},{"volume-title":"Nonsmooth analysis and control theory","year":"1998","author":"Clarke F","key":"bibr7-0142331218785694"},{"doi-asserted-by":"publisher","key":"bibr8-0142331218785694","DOI":"10.1007\/s11071-010-9915-z"},{"doi-asserted-by":"publisher","key":"bibr9-0142331218785694","DOI":"10.1049\/iet-cta.2014.0642"},{"doi-asserted-by":"publisher","key":"bibr10-0142331218785694","DOI":"10.1177\/0142331210377227"},{"doi-asserted-by":"publisher","key":"bibr11-0142331218785694","DOI":"10.1016\/j.cnsns.2014.10.008"},{"issue":"1","key":"bibr12-0142331218785694","first-page":"213","volume":"95","author":"Garrappa R","year":"2013","journal-title":"Mathematics and Computers in Simulation"},{"doi-asserted-by":"publisher","key":"bibr13-0142331218785694","DOI":"10.1109\/TAC.1979.1102073"},{"doi-asserted-by":"publisher","key":"bibr14-0142331218785694","DOI":"10.1016\/j.automatica.2009.04.003"},{"doi-asserted-by":"publisher","key":"bibr15-0142331218785694","DOI":"10.1016\/j.camwa.2009.08.019"},{"doi-asserted-by":"publisher","key":"bibr16-0142331218785694","DOI":"10.1007\/s11071-016-2872-4"},{"key":"bibr17-0142331218785694","first-page":"963","volume":"2","author":"Matignon D","year":"1996","journal-title":"Computational Engineering in Systems Applications"},{"doi-asserted-by":"publisher","key":"bibr18-0142331218785694","DOI":"10.1016\/j.automatica.2016.01.011"},{"issue":"2","key":"bibr19-0142331218785694","first-page":"597","volume":"34","author":"Mu\u00f1oz-V\u00e1zquez AJ","year":"2015","journal-title":"IMA Journal of Mathematical Control and Information"},{"doi-asserted-by":"publisher","key":"bibr20-0142331218785694","DOI":"10.1177\/0142331217737833."},{"doi-asserted-by":"publisher","key":"bibr21-0142331218785694","DOI":"10.1002\/asjc.1370"},{"doi-asserted-by":"publisher","key":"bibr22-0142331218785694","DOI":"10.1080\/00207721.2017.1348564"},{"doi-asserted-by":"publisher","key":"bibr23-0142331218785694","DOI":"10.1016\/j.sysconle.2018.04.006"},{"doi-asserted-by":"publisher","key":"bibr24-0142331218785694","DOI":"10.1007\/978-1-4419-8853-9"},{"doi-asserted-by":"publisher","key":"bibr25-0142331218785694","DOI":"10.1016\/S0947-3580(95)70014-0"},{"issue":"3","key":"bibr26-0142331218785694","first-page":"269","volume":"12","author":"Petr\u00e1\u0161 I","year":"2009","journal-title":"Fractional Calculus and Applied Analysis"},{"volume-title":"Fractional Differential Equations","year":"1999","author":"Podlubny I","key":"bibr27-0142331218785694"},{"key":"bibr28-0142331218785694","volume-title":"Real Analysis","author":"Royden HL","year":"1968","edition":"2"},{"volume-title":"Fractional Integrals and Derivatives: Theory and Applications","year":"1993","author":"Samko S","key":"bibr29-0142331218785694"},{"doi-asserted-by":"publisher","key":"bibr30-0142331218785694","DOI":"10.1016\/j.automatica.2013.11.018"},{"doi-asserted-by":"publisher","key":"bibr31-0142331218785694","DOI":"10.1177\/0142331217714306"},{"key":"bibr32-0142331218785694","first-page":"465","volume":"35","author":"Vainikko G","year":"2016","journal-title":"Journal of Analysis and its Applications"},{"doi-asserted-by":"publisher","key":"bibr33-0142331218785694","DOI":"10.1155\/2011\/635165."}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331218785694","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0142331218785694","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331218785694","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,9]],"date-time":"2024-10-09T17:55:04Z","timestamp":1728496504000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0142331218785694"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,23]]},"references-count":33,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["10.1177\/0142331218785694"],"URL":"https:\/\/doi.org\/10.1177\/0142331218785694","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"type":"print","value":"0142-3312"},{"type":"electronic","value":"1477-0369"}],"subject":[],"published":{"date-parts":[[2018,7,23]]}}}