Stability of dynamical systems : continuous, discontinuous, and discrete systems / Anthony N. Michel, Ling Hou, Derong Liu.
"Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Ebook |
| Language: | English |
| Published: |
Boston :
Birkhauser,
[2008]
|
| Series: | Systems & control.
|
| Subjects: | |
| Online Access: | Springer eBooks |
Table of Contents:
- 1.1 Dynamical Systems 1
- 1.2 A Brief Perspective on the Development of Stability Theory 4
- 1.3 Scope and Contents of the Book 6
- 2 Dynamical Systems 17
- 2.2 Dynamical Systems 19
- 2.3 Ordinary Differential Equations 20
- 2.4 Ordinary Differential Inequalities 26
- 2.5 Difference Equations and Inequalities 26
- 2.6 Differential Equations and Inclusions Defined on Banach Spaces 28
- 2.7 Functional Differential Equations 31
- 2.8 Volterra Integrodifferential Equations 34
- 2.9 Semigroups 38
- 2.10 Partial Differential Equations 46
- 2.11 Composite Dynamical Systems 51
- 2.12 Discontinuous Dynamical Systems 52
- 3 Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces 71
- 3.1 Some Qualitative Characterizations of Dynamical Systems 73
- 3.2 The Principal Lyapunov and Lagrange Stability Results for Discontinuous Dynamical Systems 82
- 3.3 The Principal Lyapunov and Lagrange Stability Results for Continuous Dynamical Systems 92
- 3.4 The Principal Lyapunov and Lagrange Stability Results for Discrete-Time Dynamical Systems 103
- 3.5 Converse Theorems for Discontinuous Dynamical Systems 112
- 3.6 Converse Theorems for Continuous Dynamical Systems 125
- 3.7 Converse Theorems for Discrete-Time Dynamical Systems 133
- 3.8 Appendix: Some Background Material on Differential Equations 137
- 4 Fundamental Theory: Specialized Stability and Boundedness Results on Metric Spaces 149
- 4.1 Autonomous Dynamical Systems 149
- 4.2 Invariance Theory 153
- 4.3 Comparison Theory 158
- 4.4 Uniqueness of Motions 165
- 5 Applications to a Class of Discrete-Event Systems 173
- 5.1 A Class of Discrete-Event Systems 173
- 5.2 Stability Analysis of Discrete-Event Systems 175
- 5.3 Analysis of a Manufacturing System 176
- 5.4 Load Balancing in a Computer Network 179
- 6 Finite-Dimensional Dynamical Systems 185
- 6.2 The Principal Stability and Boundedness Results for Ordinary Differential Equations 199
- 6.3 The Principal Stability and Boundedness Results for Ordinary Difference Equations 211
- 6.4 The Principal Stability and Boundedness Results for Discontinuous Dynamical Systems 219
- 6.5 Converse Theorems for Ordinary Differential Equations 232
- 6.6 Converse Theorems for Ordinary Difference Equations 241
- 6.7 Converse Theorems for Finite-Dimensional DDS 243
- 6.8 Appendix: Some Background Material on Differential Equations 245
- 7 Finite-Dimensional Dynamical Systems: Specialized Results 255
- 7.1 Autonomous and Periodic Systems 256
- 7.2 Invariance Theory 258
- 7.3 Domain of Attraction 263
- 7.4 Linear Continuous-Time Systems 266
- 7.5 Linear Discrete-Time Systems 285
- 7.6 Perturbed Linear Systems 295
- 7.7 Comparison Theory 316
- 7.8 Appendix: Background Material on Differential Equations and Difference Equations 320
- 8 Applications to Finite-Dimensional Dynamical Systems 337
- 8.1 Absolute Stability of Regulator Systems 338
- 8.2 Hopfield Neural Networks 344
- 8.3 Digital Control Systems 353
- 8.4 Pulse-Width-Modulated Feedback Control Systems 364
- 8.5 Digital Filters 376
- 9 Infinite-Dimensional Dynamical Systems 395
- 9.2 The Principal Lyapunov Stability and Boundedness Results for Differential Equations in Banach Spaces 398
- 9.3 Converse Theorems for Differential Equations in Banach Spaces 408
- 9.4 Invariance Theory for Differential Equations in Banach Spaces 409
- 9.5 Comparison Theory for Differential Equations in Banach Spaces 413
- 9.6 Composite Systems 415
- 9.7 Analysis of a Point Kinetics Model of a Multicore Nuclear Reactor 420
- 9.8 Results for Retarded Functional Differential Equations 423
- 9.9 Applications to a Class of Artificial Neural Networks with Time Delays 438
- 9.10 Discontinuous Dynamical Systems Determined by Differential Equations in Banach Spaces 449
- 9.11 Discontinuous Dynamical Systems Determined by Semigroups 463.