{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:34:01Z","timestamp":1767652441064,"version":"3.38.0"},"reference-count":25,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T00:00:00Z","timestamp":1343952000000},"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":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"published-print":{"date-parts":[[2012,10]]},"abstract":"<jats:p> In the present paper stabilization of a class of fractional-order unstable delay systems by fractional-order controllers is investigated. To derive the sufficient conditions for stability, an analysis based on the Nyquist stability criterion has been adopted. The analysis is carried out with fractional-order [proportional\u2013integral] and [proportional\u2013derivative] controllers to obtain the upper bound for the time delay. Furthermore, the paper proposes the conditions on the parameters of the controllers which must be fulfilled in order to have a stabilized process. Two illustrated examples using fractional-order controllers are presented for demonstrating the proposed approach. <\/jats:p>","DOI":"10.1177\/0959651812453668","type":"journal-article","created":{"date-parts":[[2012,8,4]],"date-time":"2012-08-04T04:00:30Z","timestamp":1344052830000},"page":"1166-1173","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Stabilization of fractional-order unstable delay systems by fractional-order controllers"],"prefix":"10.1177","volume":"226","author":[{"given":"Iraj","family":"Kheirizad","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Iran University of Science and Technology, Islamic Republic of Iran"}]},{"given":"Ali Akbar","family":"Jalali","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Iran University of Science and Technology, Islamic Republic of Iran"}]},{"given":"Khosro","family":"Khandani","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Iran University of Science and Technology, Islamic Republic of Iran"}]}],"member":"179","published-online":{"date-parts":[[2012,8,3]]},"reference":[{"issue":"2","key":"bibr1-0959651812453668","first-page":"493","volume":"164","author":"De Espindola JJ","year":"2005","journal-title":"Appl Math Comput"},{"volume-title":"Electromagnetic theory","year":"2007","author":"Heaviside O","key":"bibr2-0959651812453668"},{"volume-title":"Functional fractional calculus for system identification and controls","year":"2008","author":"Das S","key":"bibr3-0959651812453668"},{"key":"bibr4-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2006.06.009"},{"key":"bibr5-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.06.009"},{"key":"bibr6-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-004-3767-3"},{"key":"bibr7-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2010.10.006"},{"key":"bibr8-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1109\/9.739144"},{"key":"bibr9-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2009.07.005"},{"key":"bibr10-0959651812453668","first-page":"3182","volume-title":"2006 American control conference","author":"Xue D","year":"2006"},{"key":"bibr11-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.conengprac.2010.02.003"},{"key":"bibr12-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.enconman.2009.12.036"},{"first-page":"216","volume-title":"IEEE\/ICMA 2005","author":"Zhao C","key":"bibr13-0959651812453668"},{"key":"bibr14-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2738(83)90207-2"},{"key":"bibr15-0959651812453668","doi-asserted-by":"crossref","first-page":"1460","DOI":"10.1016\/j.camwa.2011.03.028","volume":"62","author":"Luo Y","year":"2011","journal-title":"Comput Math Applic"},{"volume-title":"Fractional calculus in bioengineering","year":"2006","author":"Magin RL","key":"bibr16-0959651812453668"},{"key":"bibr17-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.70.051915"},{"issue":"4","key":"bibr18-0959651812453668","first-page":"286","volume":"28","author":"Hwang HP","year":"1997","journal-title":"J Chin Inst Chem Eng"},{"key":"bibr19-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2007.03.002"},{"key":"bibr20-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2009.05.005"},{"key":"bibr21-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2010.03.006"},{"key":"bibr22-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtice.2010.03.001"},{"volume-title":"Fractional differential equations","year":"1999","author":"Podlubny I","key":"bibr23-0959651812453668"},{"key":"bibr24-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.06.022"},{"key":"bibr25-0959651812453668","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2010.04.011"}],"container-title":["Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651812453668","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0959651812453668","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651812453668","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T20:28:58Z","timestamp":1741033738000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0959651812453668"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,3]]},"references-count":25,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2012,10]]}},"alternative-id":["10.1177\/0959651812453668"],"URL":"https:\/\/doi.org\/10.1177\/0959651812453668","relation":{},"ISSN":["0959-6518","2041-3041"],"issn-type":[{"type":"print","value":"0959-6518"},{"type":"electronic","value":"2041-3041"}],"subject":[],"published":{"date-parts":[[2012,8,3]]}}}