{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T21:33:29Z","timestamp":1768512809605,"version":"3.49.0"},"reference-count":44,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873336"],"award-info":[{"award-number":["61873336"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61873335"],"award-info":[{"award-number":["61873335"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["2020YFB"],"award-info":[{"award-number":["2020YFB"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program","doi-asserted-by":"publisher","award":["1708200"],"award-info":[{"award-number":["1708200"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Foreign Expert Program","award":["20WZ2501100"],"award-info":[{"award-number":["20WZ2501100"]}]},{"name":"Shanghai Science and Technology Commission of Shanghai Municipality"},{"DOI":"10.13039\/501100013314","name":"111 Project","doi-asserted-by":"publisher","award":["D18003"],"award-info":[{"award-number":["D18003"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003512","name":"State Administration of Foreign Experts Affairs","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003512","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["FRF-BD-19-002A"],"award-info":[{"award-number":["FRF-BD-19-002A"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010221","name":"Higher Education Commission of Pakistan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100010221","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research Program for Universities Project","award":["10176"],"award-info":[{"award-number":["10176"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The frequency-weighted model order reduction techniques are used to find a lower-order approximation of the high-order system that exhibits high-fidelity within the frequency region emphasized by the frequency weights. In this paper, we investigate the frequency-weighted $\\mathcal{H}_2$-pseudo-optimal model order reduction problem wherein a subset of the optimality conditions for the local optimum is attempted to be satisfied. We propose two iteration-free algorithms, for the single-sided frequency-weighted case of $\\mathcal{H}_2$-model reduction, where a subset of the optimality conditions is ensured by the reduced system. In addition, the reduced systems retain the stability property of the original system. We also present an iterative algorithm for the double-sided frequency-weighted case, which constructs a reduced-order model that tends to satisfy a subset of the first-order optimality conditions for the local optimum. The proposed algorithm is computationally efficient as compared to the existing algorithms. We validate the theory developed in this paper on three numerical examples.<\/jats:p>","DOI":"10.1093\/imamci\/dnab003","type":"journal-article","created":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T05:21:04Z","timestamp":1610515264000},"page":"622-653","source":"Crossref","is-referenced-by-count":10,"title":["Frequency-weighted <i>\u210c<\/i>2-pseudo-optimal model order reduction"],"prefix":"10.1093","volume":"38","author":[{"given":"Umair","family":"Zulfiqar","sequence":"first","affiliation":[{"name":"School of Electrical, Electronics and Computer Engineering, The University of Western Australia (UWA), 35 Stirling Hwy, Crawley, WA 6009, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Victor","family":"Sreeram","sequence":"additional","affiliation":[{"name":"School of Electrical, Electronics and Computer Engineering, The University of Western Australia (UWA), 35 Stirling Hwy, Crawley, WA 6009, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mian","family":"Ilyas Ahmad","sequence":"additional","affiliation":[{"name":"Research Centre for Modelling and Simulation, National University of Sciences and Technology (NUST), Sector H-12, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mechatronic Engineering and Automation, Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, 99 Shangda Road, BaoShan District, Shanghai 200444, China"},{"name":"Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, NO. 2 North Xisanhuan Avenue Haidian District Beijing 100089, China"},{"name":"Key Laboratory of Modern Power System Simulation and Control & Renewable Energy Technology, Ministry of Education (Northeast Electric Power University), 169 Changchun Rd, Chuanying District, Jilin City 132000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"2021060309594478100_ref1","article-title":"Krylov subspace techniques for model reduction and the solution of linear matrix equations","author":"Ahmad","year":"2011"},{"key":"2021060309594478100_ref2","doi-asserted-by":"crossref","first-page":"5726","DOI":"10.1109\/ACC.2010.5531144","article-title":"Krylov subspace restart scheme for solving large-scale Sylvester equations","volume-title":"Proceedings IEEE of the 2010 American Control Conference","author":"Ahmad","year":"2010"},{"key":"2021060309594478100_ref3","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/0167-6911(86)90037-X","article-title":"Weighted hankel-norm approximation: calculation of bounds","volume":"7","author":"Anderson","year":"1986","journal-title":"Systems Control Lett."},{"key":"2021060309594478100_ref4","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/9.29422","article-title":"Controller reduction: concepts and approaches","volume":"34","author":"Anderson","year":"1989","journal-title":"IEEE Trans. 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