{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:07Z","timestamp":1787322907564,"version":"build-2736575974"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2002,1]]},"abstract":"<jats:p>\n                    Robust filtering of linear time-invariant discrete-time uncertain systems is investigated through a new parameter dependent Lyapunov matrix procedure. Its main interest relies on the fact that the Lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model. We show how to use such an approach to determine high performance H\n                    <jats:sub>2<\/jats:sub>\n                    robust filters by solving a linear problem constrained by linear matrix inequalities (LMIs). The results encompass the previous works in the quadratic Lyapunov setting. Numerical examples illustrate the theoretical results.\n                  <\/jats:p>","DOI":"10.1137\/s0363012999366308","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"700-711","source":"Crossref","is-referenced-by-count":184,"title":["Robust Filtering of Discrete-Time Linear Systems with Parameter Dependent Lyapunov Functions"],"prefix":"10.1137","volume":"41","author":[{"given":"J. C.","family":"Geromel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M. C.","family":"de Oliveira","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Bernussou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","unstructured":"B. D. O. Anderson and J. B. Moore,\n                      Optimal Filtering\n                      , Prentice Hall, Englewood Cliffs, NJ, 1979."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00939145"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(99)00035-3"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00086-5"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1109\/78.738249"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"J. C. Geromel, J. Bernussou, G. Garcia, and M. C. de Oliveira,\n                      H2andH\u221erobust filtering for discrete\u2010time linear systems\n                      , in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, 1998, pp. 632\u2013637.","DOI":"10.1109\/CDC.1998.760753"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012997327379"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1109\/9.898699"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1099-1239(199605)6:4<313::AID-RNC235>3.3.CO;2-#"},{"key":"R10","volume-title":"Observers for linear systems","author":"O\u2019Reilly John","year":"1983"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1109\/9.317138"},{"key":"R12","volume-title":"Large\u2010scale dynamic systems","author":"\u0160iljak Dragoslav","year":"1979"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.4590010206"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012999366308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:54Z","timestamp":1787319174000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012999366308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0363012999366308"],"URL":"https:\/\/doi.org\/10.1137\/s0363012999366308","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}