{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T03:04:19Z","timestamp":1787367859297,"version":"build-2736575974"},"reference-count":10,"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>We extend the method of Kazantzis and Kravaris [Systems Control Lett., 34 (1998), pp. 241--247] for the design of an observer to a larger class of nonlinear systems. The extended method is applicable to any real analytic observable nonlinear system. It is based on the solution of a first-order, singular, nonlinear PDE. This solution yields a change of state coordinates which linearizes the error dynamics. Under very general conditions, the existence and uniqueness of the solution is proved. Lyapunov's auxiliary theorem and Siegel's theorem are obtained as corollaries. The technique is constructive and yields a method for constructing approximate solutions.<\/jats:p>","DOI":"10.1137\/s0363012900375330","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"932-953","source":"Crossref","is-referenced-by-count":145,"title":["Nonlinear Observer Design in the Siegel Domain"],"prefix":"10.1137","volume":"41","author":[{"given":"Arthur J.","family":"Krener","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MingQing","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,26]]},"reference":[{"key":"R1","volume-title":"Geometrical methods in the theory of ordinary differential equations","author":"Arnol rimed V.","year":"1988"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1080\/00207178308933084"},{"key":"R3","volume-title":"Partial differential equations","author":"Evans Lawrence","year":"1998"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511626296"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(98)00017-6"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6911(83)90037-3"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6911(84)80100-0"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1137\/0323016"},{"key":"R9","unstructured":"ArthurKrener, Nonlinear stabilizability and detectability, Math. Res., Vol. 77, Akademie\u2010Verlag, Berlin, 1994, 231\u201325095g:93063"},{"key":"R10","volume-title":"Stability of motion","author":"Liapunov A.","year":"1966"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0363012900375330","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:33:09Z","timestamp":1787319189000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0363012900375330"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,1]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,1]]}},"alternative-id":["10.1137\/S0363012900375330"],"URL":"https:\/\/doi.org\/10.1137\/s0363012900375330","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,1]]}}}