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基于LMI的Lipschitz非线性不确定系统的鲁棒控制.docx

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基于LMI的Lipschitz非线性不确定系统的鲁棒控制 LMI-basedRobustControlforLipschitzNonlinearUncertainSystems Introduction: Lipschitznonlinearuncertainsystemsarewidelyusedinthefieldofcontrolengineeringduetotheirwidespreadapplicationsinpracticalsystems.Robustcontrolofsuchsystemsbecomesanimportantresearchtopicastheircomplexdynamicsanduncertainparametersmakeitdifficulttodesignastableandrobustcontroller.Inthispaper,weaimtoinvestigatetheLMI-basedrobustcontrolofLipschitznonlinearuncertainsystems. Problemformulation: TheLipschitznonlinearuncertainsystemcanbemathematicallydescribedas: dx/dt=f(x,u)+g(x,u)w wherexisthesystemstate,uisthecontrolinput,wistheuncertainty,fandgareLipschitzcontinuousfunctions.Theproblemistodesignarobustcontrollertostabilizetheuncertainsystemwithaprescribedlevelofperformanceforallpossibleuncertainties. LMI-basedrobustcontrol: Linearmatrixinequality(LMI)isapowerfultoolusedinthedesignofrobustcontrolfornonlinearuncertainsystems.TheuseofLMIprovidesasystematicapproachtodesigningcontrollersthatcanhandleuncertainties,modeluncertainties,andparametervariations. ToachievearobustcontrollerfortheLipschitznonlinearuncertainsystem,thefollowingstepsarefollowed: 1.DefineaquadraticLyapunovfunctionV(x)>0. 2.DerivecontrollawsthatminimizetheupperboundofV(x)withrespecttouncertainties. 3.UtilizeLMItechniquestoobtaintheadmissiblecontrollaws. ThecontrollercanbedesignedwithanLMI-basedrobustcontrolframeworkbyusinganH∞controlapproach.TheH∞controlapproachisapowerfulmethodfordealingwithparameteruncertaintiesinnonlinearsystemsandcanproviderobuststability.TheapproachusesLMItechniquestoreducetheupperboundofthesystem'sH∞norm,whichprovidesrobuststabilityagainstuncertainties. Conclusion: Inthispaper,wehaveinvestigatedtheLMI-basedrobustcontrolofLipschitznonlinearuncertainsystems.WehaveshownthatLMI-basedH∞controliseffectiveindesigningrobustcontrollersforsuchsystemsbyreducingtheupperboundoftheH∞normofthesystem.TheuseofLMItechniquesprovidesasystematicapproachtoachieverobuststability,whichiscriticalinpractical