Singular value decomposition for a class of linear time-varying systems with.pdf

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1、Systems&ControlLetters59(2010)792–798ContentslistsavailableatScienceDirectSystems&ControlLettersjournalhomepage:www.elsevier.com/locate/sysconleSingularvaluedecompositionforaclassoflineartime-varyingsystemswithapplicationtoswitchedlinearsystemsN.Hara∗,H.K

2、okame,K.KonishiDepartmentofElectricalandInformationSystems,OsakaPrefectureUniversity,Osaka599-8531,JapanarticleinfoabstractArticlehistory:Thepresentpaperconsiderssingularvaluedecomposition(SVD)foraclassoflineartime-varyingsystems.Received20November2009The

3、classconsideredhereindescribestime-drivenswitchedlinearsystems.BasedonanappropriateReceivedinrevisedforminput–outputdescription,thecalculationmethodofsingularvaluesandsingularvectorsisderived.The13September2010SVDenablesustocharacterizethedominantinput–ou

4、tputsignalsusingsingularvectors,whichformAccepted20September2010orthogonalsystemsininputandoutputspaces.TheSVDisthenappliedtoswitchedlinearsystemstoAvailableonline20October2010improvethetransientresponse.Anumericalexampleisprovidedtodemonstratetheproposed

5、method.©2010ElsevierB.V.Allrightsreserved.Keywords:SingularvaluedecompositionSwitchedlinearsystemFeedforwardcompensationLinearoperator1.Introductionvaluesandsingularvectors.TheSVDprovidesorthogonalinputandoutputsequencesthatenableustoapproximatetheorigina

6、lForlineardynamicalsystems,singularvaluedecompositioninfinite-dimensionalinputandoutputspacesusingafinitenumber(SVD)playsanimportantroleinanalysisandcontrol,andSVDofsingularvectors.Theclassofsystemsconsideredhereinhasbeeninvestigatedinanumberofstudies.For

7、example,modelrepresentstime-drivenswitchedlinearsystems,andweconsiderreductionmethodsforfinite-dimensionallinearsystemshavethecompensationsignaldesignproblemforswitchedlinearbeendeveloped[1,Chapters7and8],andthefinite-dimensionalsystemswithaperiodicswitch

8、inglawtoimprovethetransientapproximationproblemofaclassofinfinite-dimensionalsystemsresponseusingthenewlyestablishedSVD.Thecompensationhasbeenconsidered[2].Exactformulasforsingularvaluesandsignaldesignweconsiderinth