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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.58,NO.11,NOVEMBER20132957RobustControlforPolytopicfunction(RCLF)developedin[25],andthecontrolstoragefunctionNonlinearControlSystems(CSF)establishedin[26].Similarto[25],weconsiderthecasethattheuncertainparametersi
2、nthedriftterm,thedisturbanceinputterm,Jenq-LangWu,Member,IEEEandthecontrolinputterm,areindependent.We?rstproposeacrite-rionfortheveri?cationof-gain,fromtheexogenousinputtothecontrolledoutput,ofapolytopicnonlinearsystem.Then,wegiveaAbstract—Thistechnic
3、alnotedevelopsarobustcontrolstoragefunctionde?nitionforRCSFandderivenecessaryandsuf?cientconditionsformethodforsolvingthecontrolproblemofsingle-inputpolytopicnon-theveri?cationofRCSF.BytheproposedRCSFapproach,suf?cientlinearcontrolsystems.Necessaryand
4、suf?cientconditionsforverifyingro-conditionsfortheexistenceofcontinuousrobuststatefeedbackbustcontrolstoragefunctionsareprovided.Moreover,conditionsforthecontrollersareobtained.Itisprovedthattheobtainedsuf?cientcon-existenceofcontinuousrobuststatefeed
5、backcontrollersarederived.Anexplicitformulaforconstructingcontinuousrobustcontrollersisditionsarealsonecessaryfortheexistenceofrobustcontrollerspresented.Finally,anumericalexampleisgivenforillustration.suchthattheclosed-loopsystemhasarobuststoragefunc
6、tion(RSF)forallpossibleuncertainties.Moreover,anexplicitformulaforcon-IndexTerms—Continuoustimesystems,controlstoragefunction,control,nonlinearsystems,polytopicsystems.structingrobustcontrollersisprovided.Thetechnicalnoteisorganizedasfollows.InSection
7、II,theproblemtobesolvedisformulatedandsomepreliminariesareprovided.InSec-I.INTRODUCTIONtionIII,conditionsforverifyingRCSFsarepresentedandconditionsforguaranteeingtheexistenceofrobuststatefeedbackcontrollersOneofthemainfocusesintherobustcontrol?eldisth
8、edevelop-arederived.Moreover,anexplicitrobustfeedbacklawisgiven.mentoftechniquesandconditionsforanalysisandsynthesisofpoly-InSectionIV,anillustrativeexampleisprovided.topiclinearsystems(see,e.g.,[1],[4]–[11],[13],[17],[18],and[20]).Notations:T
