{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T23:20:24Z","timestamp":1776122424299,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T00:00:00Z","timestamp":1567987200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, classical and non-integer model order reduction methodologies are compared. Non integer order calculus has been used to generalize many classical control strategies. The property of compressing information in modelling systems, distributed in time and space, and the capability of describing long-term memory effects in dynamical systems are two features suggesting also the application of fractional calculus in model order reduction. In the paper, an open loop balanced realization is compared with three approaches based on a non-integer representation of the reduced system. Several case studies are considered and compared. The results confirm the capability of fractional order systems to capture and compress the dynamics of high order systems.<\/jats:p>","DOI":"10.3390\/e21090876","type":"journal-article","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T04:12:40Z","timestamp":1568002360000},"page":"876","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Model Order Reduction: A Comparison between Integer and Non-Integer Order Systems Approaches"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9574-7187","authenticated-orcid":false,"given":"Riccardo","family":"Caponetto","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, 95125 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"Jos\u00e9 Tenreiro","family":"Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Polytechnic of Porto, 4200-072 Porto, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emanuele","family":"Murgano","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria Elettrica Elettronica e Informatica, University of Catania, 95125 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7723-2051","authenticated-orcid":false,"given":"Maria Gabriella","family":"Xibilia","sequence":"additional","affiliation":[{"name":"Dipartimento di Ingegneria, University of Messina, 98121 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TAC.1981.1102568","article-title":"Principal component analysis in linear systems: Controllability, observability, and model reduction","volume":"26","author":"Moore","year":"1981","journal-title":"IEEE Trans. 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