nonlinear system theory - w. rugh

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1、NonlinearSystemTheoryTheVolterra/WienerApproachbyWilsonJ.RughOriginallypublishedbyTheJohnsHopkinsUniversityPress,1981(ISBNO-8018-2549-0).Webversionpreparedin2002.ContentsPREFACECHAPTER1Input/OutputRepresentationsintheTimeDomain11.1LinearSystems11.2HomogeneousNonlinearSystems31.3PolynomialandVolterr

2、aSystems181.4InterconnectionsofNonlinearSystems211.5HeuristicandMathematicalAspects341.6RemarksandReferences371.7Problems42Appendix1.1ConvergenceConditionsforInterconnectionsofVolterraSystems44Appendix1.2TheVolterraRepresentationforFunctionals49CHAPTER2Input/OutputRepresentationsintheTransformDomai

3、n542.1TheLaplaceTransform542.2LaplaceTransformRepresentationofHomogeneousSystems602.3ResponseComputationandtheAssociatedTransform682.4TheGrowingExponentialApproach752.5PolynomialandVolterraSystems812.6RemarksandReferences852.7Problems87CHAPTER3ObtainingInput/OutputRepresentationsfromDifferential-Eq

4、uationDescriptions933.1Introduction943.2ADigressiononNotation1033.3TheCarlemanLinearizationApproach1053.4TheVariationalEquationApproach1163.5TheGrowingExponentialApproach124Nth-3.6SystemsDescribedbyOrderDifferentialEquations1273.7RemarksandReferences1313.8Problems135Appendix3.1ConvergenceoftheVolte

5、rraSeriesRepresentationforLinear-AnalyticStateEquations137CHAPTER4RealizationTheory1424.1LinearRealizationTheory1424.2RealizationofStationaryHomogeneousSystems1524.3RealizationofStationaryPolynomialandVolterraSystems1634.4PropertiesofBilinearStateEquations1734.5TheNonstationaryCase1804.6RemarksandR

6、eferences1834.7Problems191Appendix4.1InterconnectionRulesfortheRegularTransferFunction194CHAPTER5ResponseCharacteristicsofStationarySystems1995.1ResponsetoImpulseInputs1995.2Steady-StateResponsetoSinusoidalInputs2015.3Steady-StateResponsetoMulti-ToneInputs2085.4ResponsetoRandomInputs2145.5TheWiener

7、OrthogonalRepresentation2335.6RemarksandReferences2465.7Problems250CHAPTER6Discrete-TimeSystems2536.1Input/OutputRepresentationsintheTimeDomain2536.2Input/OutputRepresentationsintheTransformDomain2566.3Obta