{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:37:48Z","timestamp":1760888268867,"version":"3.38.0"},"reference-count":18,"publisher":"SAGE Publications","issue":"9-10","license":[{"start":{"date-parts":[[2008,9,1]],"date-time":"2008-09-01T00:00:00Z","timestamp":1220227200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Vibration and Control"],"published-print":{"date-parts":[[2008,9]]},"abstract":"<jats:p> In this article we describe several methods for the discretization of the differintegral operator s<jats:sup>a<\/jats:sup>, where \u03b1 = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design. <\/jats:p>","DOI":"10.1177\/1077546307087445","type":"journal-article","created":{"date-parts":[[2008,9,30]],"date-time":"2008-09-30T13:57:52Z","timestamp":1222783072000},"page":"1349-1361","source":"Crossref","is-referenced-by-count":10,"title":["Discretization of Complex-order Algorithms for Control Applications"],"prefix":"10.1177","volume":"14","author":[{"given":"Ramiro S.","family":"Barbosa","sequence":"first","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida,                         431, 4200-072 Porto, Portugal,"}]},{"given":"J.A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida,                         431, 4200-072 Porto, Portugal"}]},{"given":"Manuel F.","family":"Silva","sequence":"additional","affiliation":[{"name":"Institute of Engineering of Porto, Rua Dr Antonio Bernardino de Almeida,                         431, 4200-072 Porto, Portugal"}]}],"member":"179","published-online":{"date-parts":[[2008,9,1]]},"reference":[{"doi-asserted-by":"publisher","key":"atypb1","DOI":"10.1049\/el:19930253"},{"volume-title":"Proceedings of the l6th World IFAC Congress","author":"Barbosa, R.S.","key":"atypb2"},{"doi-asserted-by":"publisher","key":"atypb3","DOI":"10.1016\/j.sigpro.2006.02.005"},{"volume-title":"Proceedings of the Second IEAC Workshop on Fractional Differentiation and its Applications","author":"Barbosa, R.S.","key":"atypb4"},{"issue":"1","key":"atypb5","first-page":"115","volume":"38","author":"Chen, Y.Q.","year":"2004","journal-title":"Nonlinear Dynamics"},{"volume-title":"Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Hartley, T.T.","key":"atypb6"},{"volume-title":"Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference","author":"Hartley, T.T.","key":"atypb7"},{"volume-title":"Proceedings of the Fifth EUROMECH Nonlinear Conference","author":"Lanusse, P.","key":"atypb8"},{"doi-asserted-by":"publisher","key":"atypb9","DOI":"10.1112\/jlms\/s2-3.2.241"},{"doi-asserted-by":"publisher","key":"atypb10","DOI":"10.1016\/j.physb.2005.01.173"},{"doi-asserted-by":"publisher","key":"atypb11","DOI":"10.1016\/j.jnoncrysol.2005.05.035"},{"volume-title":"Proceedings of the Fifth EUROMECH Nonlinear Conference","author":"Nigmatullin, R.R.","key":"atypb12"},{"volume-title":"The Fractional Calculus","year":"1974","author":"Oldham, K.B.","key":"atypb13"},{"doi-asserted-by":"publisher","key":"atypb14","DOI":"10.1109\/81.817385"},{"volume-title":"Fractional Differential Equations","year":"1999","author":"Podlubny, I.","key":"atypb15"},{"volume-title":"Fractional Integrals and Derivatives: Theory and Applications","year":"1993","author":"Samko, S.G.","key":"atypb16"},{"doi-asserted-by":"publisher","key":"atypb17","DOI":"10.1016\/j.sigpro.2006.02.024"},{"issue":"1","key":"atypb18","first-page":"47","volume":"4","author":"Tenreiro Machado, J.A.","year":"2001","journal-title":"Journal of Fractional Calculus & Applied Analysis"}],"container-title":["Journal of Vibration and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087445","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1077546307087445","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T03:35:29Z","timestamp":1741059329000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1077546307087445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9]]},"references-count":18,"journal-issue":{"issue":"9-10","published-print":{"date-parts":[[2008,9]]}},"alternative-id":["10.1177\/1077546307087445"],"URL":"https:\/\/doi.org\/10.1177\/1077546307087445","relation":{},"ISSN":["1077-5463","1741-2986"],"issn-type":[{"type":"print","value":"1077-5463"},{"type":"electronic","value":"1741-2986"}],"subject":[],"published":{"date-parts":[[2008,9]]}}}