what kinds of system can be used as tracking differentiator

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1、Proceedingsofthe29thChineseControlConferenceJuly29-31,2010,Beijing,ChinaWhatKindsofSystemCanBeUsedasTracking-Differentiator*XUEWenchao,HUANGYi,YANGXiaoxiaKeyLaboratoryofSystemsandControl,AcademyofMathematicsandSystemsScience,ChineseAcademyofSciences,Bei

2、jing100190,P.R.ChinaE-mail:xuewensuper1985@yahoo.com.cn,yhuang@amss.ac.cn,1984-yxx@163.comAbstract:Asurveyofseveralkindsdifferentiatorsisgivenfirstly.Thecomparisonshowsthetracking-differentiator(TD)permitsaweakerconditiononthestabililtyofthesystems,which

3、canbeusedtoconstructdifferentiators.Moreover,TDsetssomeweakerconstraintsontheinputsignal.ThenthepapergivestheproofsfortwokindsofsystemsthatcanbeusedtoconstructTD:oneisthesemi-globallyfinitetimestableautonomoussystem,amoregeneralkindistheonewhosecertainti

4、me-scaletransformisuniformlysemi-globallypracticallyasymptoticallystable.KeyWords:Tracking-differentiator,FilippovSolution,Semi-globallyFiniteTimeStable,UniformlySemi-globallyPracticallyAsymptoticallyStable1INTRODUCTIONAssumey(t)istheinput.Tokeepconsist

5、ence,alldifferentia-torsarediscussedundertheconditionthatthehighestorderDifferentiationofsignalsiscommonlyusedincontrolal-ofthederivativetobeestimatedisn1,i.e,thesignalstogorithms.Manyapproachesfordesigningdifferentiatorhavebeestimatedarey(i)(t);i2n1.

6、beenproposed,suchasthehigh-gainobserverbaseddif-Remark1:Forsomedifferentiators,y(i1)(t);i2n1ferentiator[1],thelineartime-derivativetrackers[2]-[3],canbenon-smooth.Inthiscase,wewillgiveanindicationtherobustexactdifferentiation[4]-[5]andthefinite-time-th

7、aty(i)(t)denotesthegeneralizedderivative.convergentdifferentiator[6],etc.Comparedwiththeabovementioneddifferentiators,thetrackingdifferentiator(TD),1)Tracking-differentiator(TD)[7][8]:whichwasfirstproposedbyJ.Q.HanandW.Wang[7],setsThesystemsusedasTD[7]:

8、aweakerconditiononthestabilityofthesystemstobecon-8structedforTD.However,arigorousproofforthegeneral>>z˙1=z2>>trackingdifferentiatorisstillopen,thoughthefilteringprop-<:::ertiesandstabilityofsomespecialkindsoftrackingdiffer->>z˙n