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基于高阶奇异值理论的LPV系统多胞分解.docx

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基于高阶奇异值理论的LPV系统多胞分解 Title:CellDecompositionofLinearParameter-VaryingSystemsbasedonHigher-orderSingularValueTheory Abstract: LinearParameter-Varying(LPV)systemsrepresentaclassofdynamicsystemswithtime-varyingparametersthatcanbedescribedwithinalinearframework.AccurateanalysisandcontrolofLPVsystemsarecrucialforvariousapplicationsinengineeringandscience.Inthispaper,weproposeacelldecompositionapproachbasedonhigher-ordersingularvaluetheorytodecomposeLPVsystemsintomultiplecells.ThisdecompositiontechniqueprovidesasystematicframeworkforstudyingtheLPVsystem'sbehaviorandfacilitatescontroldesignforcomplexLPVsystems. Introduction: LPVsystemsarewidelyusedinvariousengineeringfieldsduetotheirabilitytomodeltime-varyingdynamics.However,theanalysisandcontrolofLPVsystemsposesignificantchallengessincetheparametersvaryovertime.Celldecompositionisaneffectivemethodtohandlethesecomplexitiesbypartitioningthesystemintosmallersubsystems,knownascells,whereeachcellrepresentsaspecificregionofparametervariation.Inthispaper,weproposeacelldecompositiontechniquebasedonhigher-ordersingularvaluetheorytoenhancetheanalysisandcontrolofLPVsystems. Methods: Theproposedcelldecompositionapproachisbasedonthehigher-ordersingularvaluetheory,whichprovidesapowerfulmathematicaltooltoanalyzethebehaviorofLPVsystems.ThekeyideaistorepresenttheLPVsystemasahigher-ordersingularvaluesystemandthendecomposeitintomultiplecells.Eachcellrepresentsaspecificrangeofparametervariation,andtheLPVsystem'sdynamicswithinthatcellcanbedescribedusingthecorrespondingsingularvaluedecomposition.BydecomposingtheLPVsystemintosmallercells,wecananalyzeandcontrolthesystem'sbehaviorinamoremanageableandsystematicmanner. Results: Todemonstratetheeffectivenessoftheproposedcelldecompositiontechnique,weapplyittoacasestudyinvolvinganLPVsystem.WeshowhowtheLPVsystemcanbedecomposedintocellsbasedonvariationsinitsparameters.Furthermore,weanalyzethebehaviorofeachcellandshowhowcontroldesigncanbeperformedonindividualcells.Theresultsdemonstratethattheproposedcelld