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1、FunctionalAnalysisandLinearControlTheoryThisisVolume156inMATHEMATICSINSCIENCEANDENGINEERINGASeriesofMonographsandTextbooksEditedbyRICHARDBELLMAN,UniversityofSouthernCaliforniaThecompletelistingofbooksinthisseriesisavailablefromthePublisheruponrequest.FunctionalAnalysisandLinearCont
2、rolTheoryJ.R.LEIGHThePolytechnicofCentralLondon1980ACADEMICPRESSASubsidiaryofHarcourtBraceJovanovich.PublishersLondon*NewYork*Toronto*Sydney*SanFranciscoACADEMICPRESSINC.(LONDON)LTD.24/28OvalRoadLondonNWIUnitedStatesEditionpublishedbyACADEMICPRESSINC.111FifthAvenueNewYork,NewYork10
3、0003Copyright?1980byACADEMICPRESSINC.(LONDON)LTD.AllRightsReservedNopartofthisbookmaybereproducedinanyformbyphotostat,microfilm,oranyothermeans,withoutwrittenpermissionfromthepublishersBritishLibraryCataloguinginPublicationDataLeigh,J.R.Functionalanalysisandlinearcontroltheory.-(Ma
4、thematicsinscienceandengineering).1.Controltheory2.Functionalanalysis1.TitleII.Series629.8'32'015157QA402.380-41167ISBN0-12-441880-5PrintedinGreatBritainbyPageBros(Norwich)Ltd.,NorwichPrefaceThelasttwentyyearshaveseenarapidgrowthincontroltheorysothattherenowexistsaformidablebodyofk
5、nowledge,particularlyintheareasofmultivariablecontrolandoptimalcontrol.Bytheuseoffunctionalanalysis,aconciseconceptualframeworkcanbeputforwardforlinearcontroltheory.Withinthisframeworktheunityofthesubjectbecomesapparentandawiderangeofpowerfultheoremsbecomesapplicable.Itistheaimofth
6、isbooktoassistmathematicallyinterestedgraduateengineerstoacquirethisframework.Adifficultyforengineersindealingwithstandardmathematicaltextsistheapparentlackofmotivationinthedevelopment.Ihavetriedtomotivatethisworkbyinsertingremarksdesignedtohelpeithermotivationorvisual-ization.Math
7、ematicianswishingtoobtainaconciseoverviewofthestructureoflinearcontroltheorywillfindthebookwellsuitedtothispurpose.ForsuchreadersastartatChapter5isrecommended.Chapter1isarapidsurveyofbasicmathematics.Chapters2to5containmostofthemathematicsneededlaterinthebook,althoughsometheoremsne
8、ededonlyinChapter10aregive
