Lyapunov stability analysis for nonlinear delay systems

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1、Systems&ControlLetters42(2001)245–251www.elsevier.com/locate/sysconleLyapunovstabilityanalysisfornonlineardelaysystemsFr#ed#ericMazenca;∗,Silviu-IulianNiculescubaINRIALorraine,ProjetCONGE,ISGMPBatA,IleduSaulcy,57045MetzCedex01,FranceˆbHeudiasyc,UTC,UMRCNRS6599,BP20529,60205Compiegne,Fran

2、ce.Received9February2000;receivedinrevisedform13October2000;accepted20October2000AbstractSu/cientconditionsensuringthatanonlinearsystemwithdisturbanceshavingadelayisgloballyasymptoticallystableindependentofdelayaregiven.Theproofcarriedoutreliesextensivelyonacharacterizationofthestability

3、propertyintermsofLyapunovfunction.Theresultisappliedtosomebiologicalsystemsandneuralnetworks.Astabilizingmemorylesscontrollerforasecond-ordersystemwithstate-delayisalsoproposed.
c2001ElsevierScienceB.V.Allrightsreserved.Keywords:Lyapunovfunction;Delaysystem;Asymptoticstability1.Introduct

4、ionUsingLyapunovfunctions,weexhibitinthepresentworksu/cientconditionsensuringthatanonlinearde-Oneofthemostfundamentaltheoreticalresultslaysystemisdelayindependentandgloballyasymp-ofthenonlinearcontroltheoryistheconverseLya-toticallystable.Theyaresimpleandingeneralcanpunovtheorem.Itstates

5、thatforallasymptoticallybeeasilychecked.Observethatmostoftheworkinstablesystem,thereexistsaLyapunovfunctiontheanalysisofnonlineardelaysystemswasconcen-whosederivativealongthetrajectoriesofthesystemtratedontheuseofRazumikhin-functionapproachisnegativede;nite.Unfortunately,thedetermina-due

6、toitssimplicitytohandlein;nite-dimensionalsys-tionofexplicitformulasofLyapunovfunctionsfortem’sstabilitywith;nite-dimensionaltools.In[7]anonlinearsystemswithnospeci;cstructureisagoodoverviewonthismethodappliedtopopulationproblemwhichcannotbesolvedalways.However,dynamicsmodelsisgiven.Some

7、remarksaboutcon-notablyduringthelastdecade,manytechniquesoftrolLyapunovfunctionsbasedontheRazumikhinap-Lyapunovconstructionshavebeendevelopedforproachforasymptoticstabilitycanbefoundin[6],wideclassesofsystems.Inparticularfortwoimpor-andISSsmall-gain-basedtheoremsarepropos