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1、Birkh?userAdvancedTextsEditedbyHerbertAmann,ZürichUniversityStevenG.Krantz,WashingtonUniversity,St.LouisShrawanKumar,UniversityofNorthCarolinaatChapelHillJanNekovár,UniversitéPierreetMarieCurie,ParisYMariusTucsnakGeorgeWeissObservationandControlforOperatorSe
2、migroupsBirkh?userBasel·Boston·BerlinAuthors:MariusTucsnakGeorgeWeissInstitutElieCartan(IECN)SchoolofElectricalEngineeringNancyUniversité/CNRS/INRIAFacultyofEngineeringB.P.70239TelAvivUniversity54506Vandˉuvre-lès-NancyCedexRamatAvivFrance69978TelAvive-mail:t
3、ucsnak@iecn.u-nancy.frIsraele-mail:gweiss@eng.tau.ac.il2000MathematicsSubjectClassi?cation:47D03,93B,93CLibraryofCongressControlNumber:2008941510BibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNat
4、ionalbibliogra?e?detailedbibliographicdataisavailableintheInternetat.ISBN978-3-7643-8993-2Birkh?userVerlagAG,BaselàBostonàBerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,speci?callyther
5、ightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,reproductiononmicro?lmsorinotherways,andstorageindatabanks.Foranykindofusepermissionofthecopyrightownermustbeobtained.?2009Birkh?userVerlagAGBasel·Boston·BerlinP.O.Box133,CH-4010Base
6、l,SwitzerlandPartofSpringerScience+BusinessMediaPrintedonacid-freepaperproducedofchlorine-freepulp.TCF∞PrintedinGermanyISBN978-3-7643-8993-2e-ISBN978-3-7643-8994-9987654321www.birkhauser.chContentsPreface......................................ix1Observability
7、andControllabilityforFinite-dimensionalSystems1.1Normsandinnerproducts......................11.2Operatorson?nite-dimensionalspaces...............51.3Matrixexponentials.........................71.4Observabilityandcontrollabilityfor?nite-dimensionallinearsyste
8、ms.............................111.5TheHautustestandGramians...................152OperatorSemigroups2.1Stronglycontinuoussemigroupsandtheirgenerators.......202.2Thespectrumandtheresolventsofanop