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The design of finite\u2010time <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein state\u2010space model according to the Krein space linear estimation theory. By using the projection theory in Krein space, the finite\u2010time <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> filtering problem is solved. A numerical example is given to illustrate the performance of the <jats:italic>H<\/jats:italic><jats:sub><jats:italic>\u221e<\/jats:italic><\/jats:sub> filter.<\/jats:p>","DOI":"10.1155\/2012\/710904","type":"journal-article","created":{"date-parts":[[2012,7,13]],"date-time":"2012-07-13T20:38:15Z","timestamp":1342211895000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Finite\u2010Time <i>H<\/i><sub><i>\u221e<\/i><\/sub> Filtering for Linear Continuous Time\u2010Varying Systems with Uncertain Observations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Huihong","family":"Zhao","sequence":"first","affiliation":[]},{"given":"Chenghui","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,12]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611970760"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1974.1055174"},{"volume-title":"Control and Estimation of Systems with Input\/Output Delays","year":"2007","author":"Zhang H.","key":"e_1_2_7_3_2"},{"volume-title":"Optimal Filtering","year":"1979","author":"Anderson B. 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