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Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.<\/jats:p>","DOI":"10.1177\/0142331218798893","type":"journal-article","created":{"date-parts":[[2018,10,15]],"date-time":"2018-10-15T07:58:02Z","timestamp":1539590282000},"page":"2310-2318","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":15,"title":["Time-limited Gramians-based model order reduction for second-order form systems"],"prefix":"10.1177","volume":"41","author":[{"given":"Shafiq","family":"Haider","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, National University of Science and Technology, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdul","family":"Ghafoor","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National University of Science and Technology, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Imran","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National University of Science and Technology, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fahad Mumtaz","family":"Malik","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, National University of Science and Technology, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,10,15]]},"reference":[{"key":"bibr1-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-27909-1_7"},{"key":"bibr2-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1137\/040605552"},{"key":"bibr3-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2016.1218347"},{"key":"bibr4-0142331218798893","volume-title":"A collection of Benchmark examples for model reduction of linear time invariant dynamical systems","volume":"2","author":"Chahlaoui Y","year":"2002"},{"key":"bibr5-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-27909-1_6"},{"key":"bibr6-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.03.032"},{"key":"bibr7-0142331218798893","first-page":"31","volume-title":"International conference on modeling and simulation of microsystems semiconductors sensors and actuators (MSM 2000)","author":"Clark JV","year":"2000"},{"key":"bibr8-0142331218798893","volume-title":"An Introduction to Computer Methods","author":"Craig RJR","year":"1981"},{"key":"bibr9-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-27909-1_8"},{"key":"bibr10-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1080\/00207729008910366"},{"key":"bibr11-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1080\/00207178408933239"},{"key":"bibr12-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2014.10.013"},{"key":"bibr13-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1984.1103470"},{"key":"bibr14-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1109\/9.544000"},{"key":"bibr15-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1981.1102568"},{"key":"bibr16-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1080\/13873950701844170"},{"key":"bibr17-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1016\/S1474-6670(17)31618-X"},{"key":"bibr18-0142331218798893","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.12.013"}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331218798893","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0142331218798893","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0142331218798893","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:58:16Z","timestamp":1777647496000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0142331218798893"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,15]]},"references-count":18,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2019,5]]}},"alternative-id":["10.1177\/0142331218798893"],"URL":"https:\/\/doi.org\/10.1177\/0142331218798893","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"value":"0142-3312","type":"print"},{"value":"1477-0369","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,15]]}}}