非線性系統(tǒng)第五講無源性

NonlinearSystemsTheory

HuJiangpingSchoolofAutomationEngineeringUniversityofElectronicScienceandTechnologyofChinaE-mail:hjp_lzu@163.com精選課件Topic5Passivity5.1.Memorylessfunctions5.2.Statemodel5.3.Positiverealtransferfunction5.4.L2andLyapunovstability5.5.Feedbacksystems:passivitytheorems精選課件Topic5Passivity5.1.MemorylessfunctionsOhm'slaw:theconductanceR:theresistance精選課件Topic5PassivityNonlinearpassiveresistiveelements精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivityu精選課件Topic5Passivity5.1.Memorylessfunctions5.2.Statemodel5.3.Positiverealtransferfunction5.4.L2andLyapunovstability5.5.Feedbacksystems:passivitytheorems精選課件Topic5Passivity5.2.StatemodelExample:TheRLCcircuit精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity5.1.Memorylessfunctions5.2.Statemodel5.3.Positiverealtransferfunction5.4.L2andLyapunovstability5.5.Feedbacksystems:passivitytheorems精選課件5.3.PositiverealtransferfunctionTopic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5PassivityExercise:FindtheconditionstoensurethatthetransferfunctionisSPR1.2.3.精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity5.1.Memorylessfunctions5.2.Statemodel5.3.Positiverealtransferfunction5.4.L2andLyapunovstability5.5.Feedbacksystems:passivitytheorems精選課件Topic5PassivityIfthesystemisoutputstrictlypassivewiththenitisfinite-gainL2stable精選課件Topic5PassivityExample:Considerthep-input-p-outputsystemSupposethereisacontinuouslydifferentiablepositivesemidefinitefunctionV(x)suchthat精選課件Topic5PassivityIfV(x)satisfies精選課件Topic5Passivity5.4.L2andLyapunovstability精選課件Topic5Passivity精選課件Topic5PassivityV(x)ispositivedefinite精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity5.1.Memorylessfunctions5.2.Statemodel5.3.Positiverealtransferfunction5.4.L2andLyapunovstability5.5.Feedbacksystems:passivitytheorems精選課件Topic5Passivity5.5.Feedbacksystems:passivitytheorems精選課件Topic5PassivityCaseI:CaseII:精選課件Topic5Passivity精選課件Topic5PassivityLemma6.8Thefeedbackconnectionoftwooutputstrictlypassivesystemswithisfinite-gainL2stable精選課件Topic5PassivityTheorem6.2SupposeeachfeedbackcomponentsatisfiestheinequalityThen,theclosed-loopmapfromutoyisfinitegainL2stableifFinitegainL2stability精選課件Topic5Passivity精選課件Topic5Passivity精選課件Topic5Passivity?精選課件Topic5PassivityLyapunovstability精選課件Topic5Passivitybothfeedbackcomponentsareoutputstrictlypassiveandzero-stateobservableonecomponentisstrictlypassiveandtheotherisoutputstrictlypassivea