Robustdissipativefilt_省略_taintime_delays

Robustdissipativefilteringforcontinuous-timepolytopicuncertain

time-delaysystems

2

LVLing-ling1,,DUANGuang-ren1,WUAi-guo1

吕灵灵,段广仁,吴爱国

(1.CenterforControlTheoryandGuidanceTechnology,HarbinInstituteofTechnology,Harbin150001,China,lingling_lv@163.com;

2.InstituteofElectricPower,NorthChinaInstituteofWaterConservancyandHydroelectricPower,Zhengzhou450011,China)

Abstract:Thispaperfocusesontheproblemofdissipativefilteringforlinearcontinuous-timepolytopicuncer-taintime-delaysystems.Toobtainastableandproperlinearfiltersuchthatthefilteringerrorsystemisstrictly

dissipativeforalladmissibleuncertainties,anewdissipativitycriterionwhichrealizesseparationbetweentheLyapunovmatricesandthesystemdynamicmatricesisfirstlyprovidedintermsoflinearmatrixinequalities(LMI).ThenanLMIsufficientconditionfortheexistenceofarobustfilterisestablishedandadesignproce-dureisproposedforthistypeofsystems.Onenumericalexampledemonstrateslessconservativenessofthepro-posedcriterion,theothernumericalexampleillustratesthevalidityoftheproposedfilterdesign.Keywords:dissipativity;filtering;polytopicuncertainty;LMICLCnumber:TP273Documentcode:AArticleID:1005-9113(2010)04-0511-05

Thenotionofdissipativesystemhasplayedanim-circuit,networkandcontrolthe-portantroleinsystem,

ory.Dissipativityisageneralizationoftheconceptofpassivityinelectricalnetworkandotherdynamicalsys-temswhichdissipateenergyinsomeabstractsense[1-2].Itcontainssmallgainandpassivityasspe-cialcasesandismainlyusedforstabilityanalysisforlinearornonlinearsystems.Inrecentyears,manypa-pershaveaddressedthesynthesisproblemforL2gain,positiverealorpassivity[3-6].

Timedelayexistscommonlyindynamicsystemsduetomeasurement,transmissionandtransportlags,compu-tationaldelays,orunmodeledinertiasofsystemcompo-nents,whichhasbeengenerallyregardedasamainsourceofinstabilityandpoorperformance.Therefore,inrecentyearsconsiderableattentionhasbeendevotedtotheanalysisandsynthesisfortime-delaysystems.

Inordertoreducetheconservativenessoftradi-tionalLyapnovfunctionmethods,Feron,Apkarian,andGahinetproposedanewapproach,knownastheparameter-dependentLyapunovmethod,tothestudyof

robuststabilityofsystemswithparametricuncertain-ties.Therehasbeenaconsiderableamountofworksonextensionsandapplicationsofparameter-dependent

Lyapunovmethodtotheanalysisanddesignofrobustfiltersandcontrollers[7-10].

Astorobustdissipativity,therearesomepapersconsideringnorm-boundeduncertainsystems[11-13].

Butdissipativityresearchesonpolytopicuncertainde-

layedsystemshavenotbeenseen.Inthispaper,anewcriterionexhibitingakindofseparationbetweenthesystemmatricesandtheLyapunovmatricesisderivedandafilterdesignmethodispresented.Twonumericalexamplesarepresented.Oneshowsthattheproposedperformancecriterionislessconservativethantheonebasedonquadraticframework;theotherillustratesthefeasibilityofthedesignedfilter.

Notation1Throughoutthepresentpaper,thesuperscriptTstandsformatrixtransposition,RndenotesthendimensionalEuclideanspace,Rn×misthesetofalln×mrealmatrices,Iistheidentitymatrix,thenota-T

tionP=P>0,forP∈Rn×nmeansthatPissymmet-ricandpositivedefinite,andthesymbol"*"denotestheelementdeducedbythesymmetricproperty.1

ProblemFormaulation

Considerthefollowingcontinuous-timedelayedsystem:

x(t)=Ax(t)+Adx(t-d(t))+Bw(t)y(t)=Cx(t)+Cdx(t-d(t))+Dw(t)

,(1)

z(t)=Lx(t)+D1w(t)x(t)=φ(t),t∈[-ρ,0]

n

wherex(t)∈Risthestatevector,w(t)∈Rpisthe

y(t)∈Rmisthemeasurementoutputandnoiseinput,

z(t)∈Rpisthesignaltobeestimated.Forthissys-tem,weassumethatthedelayistime-varyingandsat-(t)≤δ<1,isfies0≤d(t)<ρ,0≤dwhereρandδ

arerealscalars,0]istheinitialvalueφ(t)∈L2[-ρ,

{

Received2008-04-11.

SponsoredbytheNationalNaturalScienceFoundationofChina(GrantNo.60710002,60974044)andSelf-plannedTaskofStateKeyLaboratoryofRo-boticsandSystem(GrantNo.SKLRS200801A03).

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