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1、SpringerMonographsinMathematicsVilmosKomornikPaolaLoretiFourierSeriesinControlTheoryVilmosKomornikPaolaLoretiInstitutdeRechercheMathe′matiqueDipartimentodiMetodieModelliAvance′eMatematiciperleScienzeApplicateUniversite′LouisPasteuretCNRSUniversita′degliStudidiRoma“LaSapienza”7,rueRene′
2、-DescartesViaA.Scarpa,1667084StrasbourgCedex00161RomaFranceItalyMathematicsSubjectClassification(2000):49-xx,93-xxLibraryofCongressCataloging-in-PublicationDataKomornik,V.Fourierseriesincontroltheory/VilmosKomornikandPaolaLoreti.p.cm.—(Springermonographsinmathematics)Includesbibliograp
3、hicalreferencesandindex.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.Thisworkmaynotbetranslatedorcop
4、iedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMediaInc.,233SpringSt.,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,com-putersoft
5、ware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisfor-bidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.Printedint
6、heUnitedStatesofAmerica.987654321SPIN1107661SpringerisapartofSpringerScience+BusinessMediaspringeronline.comPrefaceBeforeshowingtheTableofcontentsofthisbook,wewouldlikebrie?ytoexplainourmotivationtothesubject.Inthemid-eighties,J.-L.Lionscon-tributedtothemultipliermethodbyprovingpowerfu
7、landeleganttheoremsonobservability,controllability,anduniformstabilization.His1988surveyarticleandmonographalsostimulatedintensiveresearchactivityinthe?eld.Themultipliermethodledtogreatsuccess,butseveralproblemsremainedunsolved.Startingresearchonthem,wecameupwithanothere?cientwaytode
