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1、IEEETRANSACTIONSONAUTOMATICCONTROL,VOL.50,NO.10,OCTOBER20051477OnSampled-DataModelsforNonlinearSystemsJuanI.Yuz,StudentMember,IEEE,andGrahamC.Goodwin,Fellow,IEEEAbstract—Modelsfordeterministiccontinuous-timenonlinearithasbeenshownthattheyhavetobeconsideredtoobtainun-syste
2、mstypicallytaketheformofordinarydifferentialequations.biasedparameterestimates[10],[11].Toutilizethesemodelsinpracticeinvariablyrequiresdiscretiza-tion.Inthispaper,weshowhowanapproximatesampled-dataOnewouldreasonablyexpectsimilarresultstoholdfornon-modelcanbeobtainedforde
3、terministicnonlinearsystemssuchlinearsystems.However,thesituationforthenonlinearcaseisthatthelocaltruncationerrorbetweentheoutputofthismodelmorecomplexthanforlinearsystems.Indeed,tothebestofandthetruesystemisoforder1+1,where1isthesamplingourknowledge,anexplicitcharacteriz
4、ationofthesamplingzeroperiodandisthesystemrelativedegree.Theresultingmodelin-dynamicsfornonlinearsystemshaspreviouslyremainedunre-cludesextrazerodynamicswhichhavenocounterpartintheun-derlyingcontinuous-timesystem.Theideaspresentedheregener-solved,although,animplicitcharac
5、terizationhasbeengiveninalizewell-knownresultsforthelinearcase.Wealsoexplorethe[12].implicationsoftheseresultsinnonlinearsystemidentification.TheoccurrenceofnonlinearzerodynamicsisrelevanttotheIndexTerms—Nonlinearsystems,sampled-datamodels,sam-problemofcontrolofnonlinearco
6、ntinuous-timesystems.Inthisplingzeros,systemidentification,zerodynamics.context,topicssuchasrelativedegree,normalform,andzerodynamicsofthecontinuous-timenonlinearplantbecomeimpor-I.INTRODUCTIONtant,inparticular,regardingfeedbacklinearizationtechniques[13][17].Someofthesere
7、sultshavealsobeenextendedtoODELSforcontinuous-timenonlinearsystemsoftendiscrete-timeandsamplednonlinearsystems[18][30].How-Marisefromtheapplicationofphysicallawssuchasever,thetheoryforthediscrete-timecaseislesswelldevelopedconservationofmomentum,energy,etc.[1].Thesemodels
8、typ-thanforthecontinuous-timecase[31]andtheabsenceofgoodicallytaketheformofordinarydifferentiale