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1、AnalysisandControlUsingtheLambertWFunctionTIME-DELAYSYSTEMSThispageintentionallyleftblankAnalysisandControlUsingtheLambertWFunctionTIME-DELAYSYSTEMSSunYiPatrickWNelsonAGalipUlsoyUniversityofMichigan,AnnArbor,USAWorldScientificNEWJERSEY•LONDON•SINGAPORE•BEIJING•SHANGHAI•HONGKONG•TAI
2、PEI•CHENNAIPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromthe
3、BritishLibrary.TIME-DELAYSYSTEMSAnalysisandControlUsingtheLambertWFunctionCopyright©2010byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstor
4、ageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.I
5、SBN-13978-981-4307-39-0ISBN-10981-4307-39-4PrintedinSingapore.Steven-Time-DelaySystems.pmd14/20/2010,3:50PMJune2,201010:15WorldScientificBook-9inx6inSun˙mainToourfamilies,withlovevJune2,201010:15WorldScientificBook-9inx6inSun˙mainPrefaceThisbookisacollectionofrecentresearchworkonthed
6、evelopmentofananalyticalapproachforsolutionsofdelaydifferentialequationsviatheLambertWfunction.It,also,includesmethodsforanalysisandcontrolbasedonthesolutions,andtheirapplicationstomechanicalandbiologicalsystems.Delaydifferentialequationsrepresentsystemsthatincludeinherenttime-delays
7、inthesystemoradeliberateintroductionoftime-delaysforcontrolpurposes.Suchtime-delays,commoninsystemsinengineeringandscience,cancausesomesignificantproblems(e.g.,instabilityandin-accuracy)and,thus,limitanddegradetheachievableperformanceofcon-trolledsystems.However,duetotheirinnatecomp
8、lexityincludinginfinite-dim
