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In comparison with fractional-order differintegral (FOD), the distinguishing feature of the COD is that the phase slope of its Bode diagram is a function of imaginary part of the complex order of the COD. In this paper, by the use of this property of the COD, a robust control system is proposed. The design procedure and the realization of the proposed COD-based closed-loop control system are discussed. Since the phase of COD\u2019s frequency response is a nonsymmetric function of frequency, stability analysis of the proposed control system is considered a problematic task. It is proven that for the stability of the control system, it is essential that the COD be applied in a limited frequency band that is derived by the use of the Nyquist stability criterion. Finally, some numerical examples are given to demonstrate the validity and superiority of the proposed complex-order control system.<\/jats:p>","DOI":"10.1177\/0142331219836473","type":"journal-article","created":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T05:58:18Z","timestamp":1558936698000},"page":"3799-3807","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["From fractional-order to complex-order integrator loop gain: Robust control design and its stability analysis"],"prefix":"10.1177","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5430-5980","authenticated-orcid":false,"given":"Mohammad Reza","family":"Rahmani","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Iran University of Science and Technology, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali Akbar","family":"Jalali","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Iran University of Science and Technology, Iran"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2019,5,27]]},"reference":[{"key":"bibr1-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/ICCIAutom.2011.6356708"},{"key":"bibr2-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2008.12.014"},{"key":"bibr3-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/ISIE.2010.5637621"},{"key":"bibr4-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-50249-6"},{"key":"bibr5-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1177\/1077546310388002"},{"key":"bibr6-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/28.806058"},{"key":"bibr7-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/28.845057"},{"key":"bibr8-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.08.007"},{"key":"bibr9-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1177\/1077546307087433"},{"key":"bibr10-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/28.806058"},{"key":"bibr11-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2008.09.041"},{"key":"bibr12-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2017.08.2093"},{"key":"bibr13-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/41.382137"},{"key":"bibr14-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/IAS.2003.1257841"},{"key":"bibr15-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1109\/IranianCEE.2012.6292481"},{"key":"bibr16-0142331219836473","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2012.659696"},{"key":"bibr17-0142331219836473","unstructured":"Lanusse P (2010) CRONE Control System Design, a CRONE toolbox for Matlab. 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