{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T18:14:19Z","timestamp":1779387259969,"version":"3.53.1"},"reference-count":38,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271426"],"award-info":[{"award-number":["12271426"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009110","name":"Natural Science Foundation of Xinjiang Uygur Autonomous Region","doi-asserted-by":"publisher","award":["2023D01C163"],"award-info":[{"award-number":["2023D01C163"]}],"id":[{"id":"10.13039\/100009110","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015401","name":"Key Research and Development Projects of Shaanxi Province","doi-asserted-by":"publisher","award":["2023-YBSF-399"],"award-info":[{"award-number":["2023-YBSF-399"]}],"id":[{"id":"10.13039\/501100015401","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100017596","name":"Natural Science Basic Research Plan in Shaanxi Province of China","doi-asserted-by":"publisher","award":["2022JQ-067"],"award-info":[{"award-number":["2022JQ-067"]}],"id":[{"id":"10.13039\/501100017596","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Tianchi Talent Introduction Plan Project of Xinjiang Uyghur Autonomous Region"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:p>\n                    This paper focuses on the\n                    <jats:italic toggle=\"yes\">H<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    optimal model reduction problem of positive systems. According to the coefficient matrices of the positive system, the nonnegative orthonormal matrix is taken as the projection matrix, and the\n                    <jats:italic toggle=\"yes\">H<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    optimal model reduction problem is developed. Since the projection matrix is orthonormal and nonnegative, the\n                    <jats:italic toggle=\"yes\">H<\/jats:italic>\n                    <jats:sub>2<\/jats:sub>\n                    optimal model reduction problem is reformulated as a constrained optimization problem defined on the Stiefel manifold, and further regarded as a constrained optimization problem defined on the oblique manifold. By the augmented Lagrangian function, the constrained optimization problem defined on the oblique manifold is tackled by employing the Dai-Yuan-type conjugate gradient method to solve a series of unconstrained optimization subproblems. When the objective function of a subproblem satisfies some conditions, the iterative sequence produced by the conjugate gradient method is convergent. Finally, numerical experiments illustrate the efficiency of the proposed model reduction method.\n                  <\/jats:p>","DOI":"10.1177\/01423312251319586","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T07:43:04Z","timestamp":1741851784000},"page":"1667-1677","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["<i>H<\/i>\n                    <sub>2<\/sub>\n                    optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold"],"prefix":"10.1177","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5443-8193","authenticated-orcid":false,"given":"Ping","family":"Yang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, China"},{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0185-7765","authenticated-orcid":false,"given":"Zhao-Hong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5541-1136","authenticated-orcid":false,"given":"Yao-Lin","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University,China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1515\/9781400830244"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.01.040"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718713"},{"issue":"1","key":"e_1_3_2_5_1","first-page":"1455","article-title":"Manopt, a MATLAB toolbox for optimization on manifolds","volume":"15","author":"Boumal N","year":"2014","unstructured":"Boumal N, Mishra B, Absil PA, et al. 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