{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T02:13:35Z","timestamp":1767665615550,"version":"3.38.0"},"reference-count":28,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2011,8,29]],"date-time":"2011-08-29T00:00:00Z","timestamp":1314576000000},"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":[[2012,2]]},"abstract":"<jats:p> This paper studies the consensus problems of fractional-order systems with non-uniform input and communication delays over directed static networks. Based on a frequency-domain approach and generalized Nyquist stability criterion, sufficient conditions are obtained to ensure the consensus of the fractional-order systems with simultaneously non-uniform input and communication delays. When the fractional-order [Formula: see text], it is found that the consensus condition is dependent on input delays but independent on communication delays. Surprisingly, when there is no input delay, consensus can be realized whatever the communication delays are. However, a counter-example shows that communication delays will have a great influence on the consensus condition when the fractional-order [Formula: see text]. Moreover, the bounds of input and communication delays are explicitly given to guarantee the consensus of the delayed fractional-order systems with fractional-order [Formula: see text] under an undirected interaction graph. <\/jats:p>","DOI":"10.1177\/0959651811412132","type":"journal-article","created":{"date-parts":[[2011,8,30]],"date-time":"2011-08-30T02:08:05Z","timestamp":1314670085000},"page":"271-283","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":44,"title":["Consensus of fractional-order systems with non-uniform input and communication delays"],"prefix":"10.1177","volume":"226","author":[{"given":"J","family":"Shen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Southeast University, Nanjing, People\u2019s Republic of China"}]},{"given":"J","family":"Cao","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southeast University, Nanjing, People\u2019s Republic of China"}]},{"given":"J","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Southeast University, Nanjing, People\u2019s Republic of China"}]}],"member":"179","published-online":{"date-parts":[[2011,8,29]]},"reference":[{"key":"bibr1-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1147"},{"key":"bibr2-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.895842"},{"key":"bibr3-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.864190"},{"key":"bibr4-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.834433"},{"key":"bibr5-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2006.872761"},{"key":"bibr6-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.930184"},{"key":"bibr7-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.80.066121"},{"key":"bibr8-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1080\/00207170600825097"},{"key":"bibr9-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2044274"},{"key":"bibr10-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2004.834113"},{"key":"bibr11-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.03.006"},{"volume-title":"The fractional calculus","year":"1974","author":"Oldham K.","key":"bibr12-0959651811412132"},{"issue":"2","key":"bibr13-0959651811412132","first-page":"362","volume":"40","author":"Cao Y.","year":"2009","journal-title":"IEEE Trans. Syst. Man Cybernet., Part B: Cybernet."},{"key":"bibr14-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1122\/1.549887"},{"key":"bibr15-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2010.01.008"},{"key":"bibr16-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-006-9094-0"},{"key":"bibr17-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016591006562"},{"key":"bibr18-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00306-5"},{"key":"bibr19-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2007.03.017"},{"key":"bibr20-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1980.1102280"},{"volume-title":"Fractional differential equations","year":"1999","author":"Podlubny I.","key":"bibr21-0959651811412132"},{"key":"bibr22-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90486-3"},{"key":"bibr23-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2005.846556"},{"volume-title":"Matrix analysis","year":"1990","author":"Horn R.","key":"bibr24-0959651811412132"},{"key":"bibr25-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.003"},{"key":"bibr26-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.08.019"},{"key":"bibr27-0959651811412132","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2010.2045891"},{"first-page":"4765","volume-title":"In Proceedings of the 48th IEEE Conference on Decision and control","author":"M\u00fcnz U.","key":"bibr28-0959651811412132"}],"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\/0959651811412132","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0959651811412132","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0959651811412132","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T07:26:44Z","timestamp":1741073204000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0959651811412132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,8,29]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2012,2]]}},"alternative-id":["10.1177\/0959651811412132"],"URL":"https:\/\/doi.org\/10.1177\/0959651811412132","relation":{},"ISSN":["0959-6518","2041-3041"],"issn-type":[{"type":"print","value":"0959-6518"},{"type":"electronic","value":"2041-3041"}],"subject":[],"published":{"date-parts":[[2011,8,29]]}}}