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一类切换广义系统的H2H∞控制 Title:H2H∞ControlforSwitchingGeneralizedSystems Abstract: TheH2H∞controlproblemforswitchinggeneralizedsystemshasgainedsignificantattentioninrecentyearsduetoitsapplicabilityinvariousfields,suchaspowersystems,robotics,andaerospaceengineering.Thispaperaimstoprovideacomprehensiveoverviewofthetheoreticalfoundations,systemmodeling,controldesign,andoptimizationtechniquesrelatedtoH2H∞controlforswitchinggeneralizedsystems.Additionally,severalcasestudiesarepresentedtoillustratetheefficacyofthiscontrolapproachinpracticalapplications. 1.Introduction Switchinggeneralizedsystemsrefertodynamicalsystemsthatcanswitchamongafinitenumberofmodes.TheH2H∞controlproblemisconcernedwithdesigningcontrolstrategiesthatensurebothboundeddisturbancesattenuation(H2)androbuststability(H∞)forsuchsystems.Thiscontrolapproachisparticularlyimportantinthepresenceofuncertainties,variations,andmode-switchingphenomena. 2.MathematicalModelingofSwitchingGeneralizedSystems Thissectionaddressesthemathematicalrepresentationofswitchinggeneralizedsystems.Theconceptsofmodetransition,mode-dependentandmode-independentmatrices,andmodeactivationsequencesareintroduced.Differentmodelingtechniques,suchashybridautomataandswitchedsystemstheory,forcharacterizingthedynamicsofthesesystemsarediscussed. 3.H2H∞AnalysisforSwitchingGeneralizedSystems ThissectionfocusesontheanalysistoolsandmethodsemployedinH2H∞control.TheH2andH∞performancecriteriaaredefined,followedbytheintroductionoflinearmatrixinequalities(LMIs)andexponentialstabilityconditionsforensuringrobuststability.TheconceptofthecommonLyapunovfunction(CLF)isalsoexploredinrelationtoswitchedsystems. 4.ControllerDesignforSwitchingGeneralizedSystems ThedesignofH2H∞controllersforswitchinggeneralizedsystemsisdiscussedinthissection.Approachessuchasmode-dependentcontrollerdesign,mode-independentcontrollerdesign,andmixedcontrollerdesignarepresented.Thesynthesisofcontrollersusingoptimizationtechniques,includingconvexoptimizationandgeneticalgorithms,isalsoelaboratedupon.