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Preface xi
Introduction 1
Dynamical Systems 1
A Brief Perspective on the Development of Stability Theory 4
Scope and Contents of the Book 6
Bibliography 12
Dynamical Systems 17
Notation 18
Dynamical Systems 19
Ordinary Differential Equations 20
Ordinary Differential Inequalities 26
Difference Equations and Inequalities 26
Differential Equations and Inclusions Defined on Banach Spaces 28
Functional Differential Equations 31
Volterra Integrodifferential Equations 34
Semigroups 38
Partial Differential Equations 46
Composite Dynamical Systems 51
Discontinuous Dynamical Systems 52
Notes and References 59
Problems 61
Bibliography 67
Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces 71
Some Qualitative Characterizations of Dynamical Systems 73
The Principal Lyapunov and Lagrange Stability Results for Discontinuous Dynamical Systems 82
The Principal Lyapunov and LagrangeStability Results for Continuous Dynamical Systems 92
The Principal Lyapunov and Lagrange Stability Results for Discrete-Time Dynamical Systems 103
Converse Theorems for Discontinuous Dynamical Systems 112
Converse Theorems for Continuous Dynamical Systems 125
Converse Theorems for Discrete-Time Dynamical Systems 133
Appendix: Some Background Material on Differential Equations 137
Notes and References 141
Problems 142
Bibliography 147
Fundamental Theory: Specialized Stability and Boundedness Results on Metric Spaces 149
Autonomous Dynamical Systems 149
Invariance Theory 153
Comparison Theory 158
Uniqueness of Motions 165
Notes and References 167
Problems 167
Bibliography 172
Applications to a Class of Discrete-Event Systems 173
A Class of Discrete-Event Systems 173
Stability Analysis of Discrete-Event Systems 175
Analysis of a Manufacturing System 176
Load Balancing in a Computer Network 179
Notes and References 181
Problems 181
Bibliography 182
Finite-Dimensional Dynamical Systems 185
Preliminaries 185
The Principal Stability and Boundedness Results for Ordinary Differential Equations 199
The Principal Stability and Boundedness Results for Ordinary Difference Equations 211
The Principal Stability and Boundedness Results for Discontinuous Dynamical Systems 219
Converse Theorems for Ordinary Differential Equations 232
Converse Theorems for Ordinary Difference Equations 241
Converse Theorems for Finite-Dimensional DDS 243
Appendix: Some Background Material on Differential Equations 245
Notes and References 249
Problems 250
Bibliography 253
Finite-Dimensional Dynamical Systems: Specialized Results 255
Autonomous and Periodic Systems 256
Invariance Theory 258
Domain of Attraction 263
Linear Continuous-Time Systems 266
Linear Discrete-Time Systems 285
Perturbed Linear Systems 295
Comparison Theory 316
Appendix: Background Material on Differential Equations and Difference Equations 320
Notes and References 328
Problems 329
335
Applications to Finite-Dimensional Dynamical Systems 337
Absolute Stability of Regulator Systems 338
Hopfield Neural Networks 344
Digital Control Systems 353
Pulse-Width-Modulated Feedback Control Systems 364
Digital Filters 376
Notes and References 387
Bibliography 389
Infinite-Dimensional Dynamical Systems 395
Preliminaries 396
The Principal Lyapunov Stability and Boundedness Results for Differential Equations in Banach Spaces 398
Converse Theorems for Differential Equations in Banach Spaces 408
Invariance Theory for Differential Equations in Banach Spaces 409
Comparison Theory for Differential Equations in Banach Spaces 413
Composite Systems 415
Analysis of a Point Kinetics Model of a Multicore Nuclear Reactor 420
Results for Retarded Functional Differential Equations 423
Applications to a Class of Artificial Neural Networks with Time Delays 438
Discontinuous Dynamical Systems Determined by Differential Equations in Banach Spaces 449
Discontinuous Dynamical Systems Determined by Semigroups 463
Notes and References 479
Problems 480
Bibliography 486
Index 489
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Michael P Napier
reviewed Stability of Dynamical Systems: Continuous, Discontinuous, and Discrete Systems on August 22, 2014
Stability of Dynamical Systems
Great Epistemological Approach to Popular Science
Learning more about stars, black holes and dark matter is a great part of the fun in this book, but I don't think it's the most important lesson I take from it.
Its Epistemological approach, its theory of how we know and learn things, is fascinating. First of all, by insisting on the question "how do they know that?", feeding this scientific curiosity. It then lays down its scheme of three universes: the perceived, the detected and the theoretical and how they interact with each order while we explore the nature of the universe itself. By setting this scenario, it guides us on presenting the most intriguing phenomena of astronomy and cosmology while also explaining how the experiments were performed to verify theories or how new measurements set new theories forward.
I have a background in engineering which helped me comprehend the physics and little mathematical details covered by the authors, but I believe that any motivated layperson might enjoy the reading.
It satiated my curiosity about how dark matter and dark energy became a topic of studies but also gave me tools on how to deal with scientific communication of daily life.
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