Linear dynamical systems

목차 (Table of Contents)

• CONTENTS
• Preface to the Revised Edition = xi
• Preface to the First Edition = xiii
• Chapter 1 Basic Concepts, Problems, and Examples
• 1.1 Dynamical Systems, Inputs, and Outputs = 1
• 1.2 Internal Description of ∑ = 3
• 1.3 Realizations = 6
• 1.4 Controllability and Observability = 7
• 1.5 Stability and Feedback = 11
• 1.6 Optimality = 13
• 1.7 Stochastic Disturbances = 17
• Notes and Refcrences = 19
• Chapter 2 Mathematical Description of Linear Dynamical Systems
• 2.1 Introduction = 21
• 2.2 Dynamical Systems = 21
• 2.3 External Description = 27
• 2.4 Frequency-Domain Analysis = 28
• 2.5 Transfer Functions = 30
• 2.6 Impulse-Response Function = 31
• Notes and References = 33
• Chapter 3 Control1ability and Reachability
• 3.1 Introduction = 35
• 3.2 Basic Definitions = 36
• 3.3 Time-Dependent Linear Systems = 39
• 3.4 Discrete-Time Systems = 43
• 3.5 Constant Systems = 47
• 3.6 Positive Controllability = 52
• 3.7 Relative Controllability = 55
• 3.8 Conditional Controllability = 57
• 3.9 Structural Controllability = 58
• 3.10 Controllability and Transfer Functions = 61
• 3.11 Systems with a Delay = 62
• Miscellaneous Exercises = 64
• Notes and References = 68
• Chapter 4 Obserwability / Constructibility
• 4.1 Introduction = 72
• 4.2 Basic Definitions = 73
• 4.3 Basic Theorems = 75
• 4.4 Duality = 81
• 4.5 Functional Analytic Approach to Observability = 82
• 4.6 The Problem of Moments = 83
• Miscellaneous Exercises = 84
• Notes and References = 85
• Chapter 5 Structure Theorems and Canonical Forms
• 5.1 Introduction = 88
• 5.2 State Variable Transformations = 90
• 5.3 Control Canonical Forms = 91
• 5.4 Observer Canonical Forms = 97
• 5.5 Invariance of Transfer Functions = 99
• 5.6 Canonical Forms and the Bezoutiant Matrix = 101
• 5.7 The Feedback Group and Invariant Theory = 104
• Miscellaneous Exercises = 111
• Notes and References = 114
• Chapter 6 Realization Theory
• 6.1 Introduction = 117
• 6.2 Algebraic Equivalence and Minimal Realizability = 118
• 6.3 Construction of Roalizations = 124
• 6.4 Minimal Realization Algorithm = 127
• 6.5 Examples = 128
• 6.6 Realization of Transfer Functions = 131
• 6.7 Uniqucness of Minimal Realizations = 132
• 6.8 Partial Roalizations = 133
• 6.9 Reduced Order Models and Balanced Realizations = 138
• Miscellaneous Excrcises = 140
• Notes and References = 145
• Chapter 7 Stability Theory
• 7.1 Introduction = 147
• 7.2 Some Examples and Basic Concepts = 149
• 7.3 Routh-Hurwicz Methods = 152
• 7.4 Lyapunov Method = 156
• 7.5 Frequency-Domain Techniques = 162
• 7.6 Feedback Control Systems and Stability = 164
• 7.7 Modal Control = 169
• 7.8 Observers = 173
• 7.9 Structural Stability = 174
• Miscellaneous Exercises = 177
• Notes and References = 179
• Chapter 8 The Linear-Quadratic-Gaussian Problem
• 8.1 Motivation and Examples = 182
• 8.2 Open-Loop Solutions = 185
• 8.3 The Maximum Principle = 187
• 8.4 Some Computational Considerations = 190
• 8.5 Feedback Solutions = 192
• 8.6 Generalized X-Y Functions = 196
• 8.7 Optimality versus Stability = 204
• 8.8 A Low-Dimensional Alternative to the Algebraic Riccati Equation = 214
• 8.9 Computational Approaches for Riccati Equations = 216
• 8.10 Structural Stability of the Optimal Closed-Loep System = 219
• 8.11 Inverse Problems = 220
• 8.12 Linear Filtering Theory and Duality = 227
• 8.13 The Separation Principle and Stochastic Control Theory = 231
• 8.14 Discrete-Time Problems = 233
• 8.15 Generalized X-Y Functions Revisited = 234
• Miscellaneous Exercises = 235
• Notes and References = 240
• Chapter 9 A Geometric-Algebraic View of Linear Systems
• 9.1 Algebra, Geometry, and Linear Systems = 246
• 9.2 Mathematical Description of a Linear System = 247
• 9.3 The Module Structure of Ω, Γ, and X = 249
• 9.4 Some System-Theoretic Consequences = 253
• 9.5 Transfer Functions = 257
• 9.6 Realization of Transfer Functions = 260
• 9.7 The Construction of Canonical Realizations = 263
• 9.8 Partial Realizations = 271
• 9.9 Pole-Shifting and Stability = 273
• 9.10 Systems over Rings = 274
• 9.11 Some Geometric Aspects of Linear Systems = 278
• 9.12 Feedback, the McMillan Degree, and Kronecker Indices = 283
• 9.13 Some Additional Ideas from Algebraic Geometry = 285
• 9.14 Pole Placement for Lincar Regulaton = 288
• 9.15 Multivariable Nyquist Criteria = 291
• 9.16 Algebraic Topology and Simplicial Complcx of ∑ = 292
• Miscellaneous Exercises = 298
• Notes and References = 310
• Chapter 10 Infinite-Dimensional Systems
• 10.1 Finiteness as a System Property = 317
• 10.2 Reachability and Controllability = 319
• 10.3 Observability and Duality = 323
• 10.4 Stability Theory = 325
• 10.5 Realization Theory = 327
• 10.6 The LQG Problem = 330
• 10.7 Operator Riccati Equations and Generalized X-Y Functions = 332
• Miscellaneous Exercises = 335
• Notes and References = 345
• Index = 347