Nonlinear system theory(BOOK)

Nonlinear system theory(BOOK) - Nonlinear System Theory The...

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Unformatted text preview: Nonlinear System Theory The Volterra/Wiener Approach by Wilson J. Rugh Originally published by The Johns Hopkins University Press, 1981 ( ISBN O-8018-2549-0 ). Web version prepared in 2002. Contents PREFACE CHAPTER 1 Input/Output Representations in the Time Domain 1 1.1 Linear Systems 1 1.2 Homogeneous Nonlinear Systems 3 1.3 Polynomial and Volterra Systems 18 1.4 Interconnections of Nonlinear Systems 21 1.5 Heuristic and Mathematical Aspects 34 1.6 Remarks and References 37 1.7 Problems 42 Appendix 1.1 Convergence Conditions for Interconnections of Volterra Systems 44 Appendix 1.2 The Volterra Representation for Functionals 49 CHAPTER 2 Input/Output Representations in the Transform Domain 54 2.1 The Laplace Transform 54 2.2 Laplace Transform Representation of Homogeneous Systems 60 2.3 Response Computation and the Associated Transform 68 2.4 The Growing Exponential Approach 75 2.5 Polynomial and Volterra Systems 81 2.6 Remarks and References 85 2.7 Problems 87 CHAPTER 3 Obtaining Input/Output Representations from Differential-Equation Descriptions 93 3.1 Introduction 94 3.2 A Digression on Notation 103 3.3 The Carleman Linearization Approach 105 3.4 The Variational Equation Approach 116 3.5 The Growing Exponential Approach 124 3.6 Systems Described by th N − Order Differential Equations 127 3.7 Remarks and References 131 3.8 Problems 135 Appendix 3.1 Convergence of the Volterra Series Representation for Linear-Analytic State Equations 137 CHAPTER 4 Realization Theory 142 4.1 Linear Realization Theory 142 4.2 Realization of Stationary Homogeneous Systems 152 4.3 Realization of Stationary Polynomial and Volterra Systems 163 4.4 Properties of Bilinear State Equations 173 4.5 The Nonstationary Case 180 4.6 Remarks and References 183 4.7 Problems 191 Appendix 4.1 Interconnection Rules for the Regular Transfer Function 194 CHAPTER 5 Response Characteristics of Stationary Systems 199 5.1 Response to Impulse Inputs 199 5.2 Steady-State Response to Sinusoidal Inputs 201 5.3 Steady-State Response to Multi-Tone Inputs 208 5.4 Response to Random Inputs 214 5.5 The Wiener Orthogonal Representation 233 5.6 Remarks and References 246 5.7 Problems 250 CHAPTER 6 Discrete-Time Systems 253 6.1 Input/Output Representations in the Time Domain 253 6.2 Input/Output Representations in the Transform Domain 256 6.3 Obtaining Input/Output Representations from State Equations 263 6.4 State-Affine Realization Theory 269 6.5 Response Characteristics of Discrete-Time Systems 277 6.6 Bilinear Input/Output Systems 287 6.7 Two-Dimensional Linear Systems 292 6.8 Remarks and References 298 6.9 Problems 301 CHAPTER 7 Identification 303 7.1 Introduction 303 7.2 Identification Using Impulse Inputs 305 7.3 Identification Based on Steady-State Frequency Response 308 7.4 Identification Using Gaussian White Noise Inputs 313 7.5 Orthogonal Expansion of the Wiener Kernels 322 7.6 Remarks and References 326 7.7 Problems 329...
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This note was uploaded on 10/16/2011 for the course MECHATRONI 111 taught by Professor Jung during the Spring '11 term at Hanyang University.

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Nonlinear system theory(BOOK) - Nonlinear System Theory The...

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