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1、SpringerMonographsinMathematicsVilmosKomornikPaolaLoretiFourierSeriesinControlTheoryVilmosKomornikPaolaLoretiInstitutdeRechercheMathe´matiqueDipartimentodiMetodieModelliAvance´eMatematiciperleScienzeApplicateUniversite´LouisPasteuretCNRSUniversita´degliStudidiRoma“LaSapienza”7,rueRene´-Descar
2、tesViaA.Scarpa,1667084StrasbourgCedex00161RomaFranceItalyMathematicsSubjectClassification(2000):49-xx,93-xxLibraryofCongressCataloging-in-PublicationDataKomornik,V.Fourierseriesincontroltheory/VilmosKomornikandPaolaLoreti.p.cm.—(Springermonographsinmathematics)Includesbibliographicalreference
3、sandindex.ISBN0-387-22383-5(alk.paper)1.Controltheory.2.Fourierseries.I.Loreti,Paola.II.Title.III.Series.QA402.3.K57852004003′.5—dc222004056525ISBN0-387-22383-5Printedonacid-freepaper.©2005SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwit
4、houtthewrittenpermissionofthepublisher(SpringerScience+BusinessMediaInc.,233SpringSt.,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,com-putersoftware,orbysimilarordissimilar
5、methodologynowknownorhereafterdevelopedisfor-bidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.987654321SP
6、IN1107661SpringerisapartofSpringerScience+BusinessMediaspringeronline.comPrefaceBeforeshowingtheTableofcontentsofthisbook,wewouldlikebrieflytoexplainourmotivationtothesubject.Inthemid-eighties,J.-L.Lionscon-tributedtothemultipliermethodbyprovingpowerfulandeleganttheoremsonobservability,control
7、lability,anduniformstabilization.His1988surveyarticleandmonographalsostimulatedintensiveresearchactivityinthefield.Themultipliermethodledtogreatsuccess,butseveralproblemsremainedunsolved.Startingresearchonthem,wecameupwithanotherefficientwaytode
