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Two new <jats:italic>frequency-dependent balanced truncation<\/jats:italic> methods are developed, one is <jats:italic>single-frequency (SF)-type frequency-dependent balanced truncation<\/jats:italic> to cope with the cases that only a single dominating point of the operating frequency interval is pre-known, and the other is <jats:italic>interval-type frequency-dependent balanced truncation<\/jats:italic> to deal with the case that both the upper and lower bounds of the relevant frequency interval are known a priori. Error bounds for both approaches are derived to estimate the approximation error over a pre-specified frequency interval. In contrast to other error bounds for frequency-weighted or frequency-limited balanced truncation, these bounds are given specifically for the interval under consideration and are thus often sharper than the global bounds for previous methods. We show that the new methods generally lead to good in-band approximation performance, and at the same time provide accurate error bounds under certain conditions. Examples are included for illustration.<\/jats:p>","DOI":"10.1007\/s10444-020-09823-w","type":"journal-article","created":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T13:17:47Z","timestamp":1605532667000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Balanced truncation of linear time-invariant systems over finite-frequency ranges"],"prefix":"10.1007","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3362-4103","authenticated-orcid":false,"given":"Peter","family":"Benner","sequence":"first","affiliation":[]},{"given":"Xin","family":"Du","sequence":"additional","affiliation":[]},{"given":"Guanghong","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Dan","family":"Ye","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"9823_CR1","doi-asserted-by":"crossref","unstructured":"Antoulas, A.C.: Approximation of large-scale dynamical systems, SIAM Publications, Philadelphia (2005)","DOI":"10.1137\/1.9780898718713"},{"issue":"4","key":"9823_CR2","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s11831-014-9111-2","volume":"21","author":"U Baur","year":"2014","unstructured":"Baur, U., Benner, P., Feng, L.: Model order reduction for linear and nonlinear systems: A system-theoretic perspective. 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