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...
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| Main Authors: | , , |
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| Format: | Ebook |
| Language: | English |
| Published: |
Boston :
Birkhauser,
[2008]
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| Series: | Systems & control.
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| Subjects: | |
| Online Access: | Springer eBooks |
MARC
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| 100 | 1 | |a Michel, Anthony N., |e author. |9 1083211 | |
| 245 | 1 | 0 | |a Stability of dynamical systems : |b continuous, discontinuous, and discrete systems / |c Anthony N. Michel, Ling Hou, Derong Liu. |
| 264 | 1 | |a Boston : |b Birkhauser, |c [2008] | |
| 264 | 4 | |c ©2008 | |
| 300 | |a 1 online resource (xii, 501 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Systems & control : foundations & applications | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |g 1.1 |t Dynamical Systems |g 1 -- |g 1.2 |t A Brief Perspective on the Development of Stability Theory |g 4 -- |g 1.3 |t Scope and Contents of the Book |g 6 -- |g 2 |t Dynamical Systems |g 17 -- |g 2.2 |t Dynamical Systems |g 19 -- |g 2.3 |t Ordinary Differential Equations |g 20 -- |g 2.4 |t Ordinary Differential Inequalities |g 26 -- |g 2.5 |t Difference Equations and Inequalities |g 26 -- |g 2.6 |t Differential Equations and Inclusions Defined on Banach Spaces |g 28 -- |g 2.7 |t Functional Differential Equations |g 31 -- |g 2.8 |t Volterra Integrodifferential Equations |g 34 -- |g 2.9 |t Semigroups |g 38 -- |g 2.10 |t Partial Differential Equations |g 46 -- |g 2.11 |t Composite Dynamical Systems |g 51 -- |g 2.12 |t Discontinuous Dynamical Systems |g 52 -- |g 3 |t Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces |g 71 -- |g 3.1 |t Some Qualitative Characterizations of Dynamical Systems |g 73 -- |g 3.2 |t The Principal Lyapunov and Lagrange Stability Results for Discontinuous Dynamical Systems |g 82 -- |g 3.3 |t The Principal Lyapunov and Lagrange Stability Results for Continuous Dynamical Systems |g 92 -- |g 3.4 |t The Principal Lyapunov and Lagrange Stability Results for Discrete-Time Dynamical Systems |g 103 -- |g 3.5 |t Converse Theorems for Discontinuous Dynamical Systems |g 112 -- |g 3.6 |t Converse Theorems for Continuous Dynamical Systems |g 125 -- |g 3.7 |t Converse Theorems for Discrete-Time Dynamical Systems |g 133 -- |g 3.8 |t Appendix: Some Background Material on Differential Equations |g 137 -- |g 4 |t Fundamental Theory: Specialized Stability and Boundedness Results on Metric Spaces |g 149 -- |g 4.1 |t Autonomous Dynamical Systems |g 149 -- |g 4.2 |t Invariance Theory |g 153 -- |g 4.3 |t Comparison Theory |g 158 -- |g 4.4 |t Uniqueness of Motions |g 165 -- |g 5 |t Applications to a Class of Discrete-Event Systems |g 173 -- |g 5.1 |t A Class of Discrete-Event Systems |g 173 -- |g 5.2 |t Stability Analysis of Discrete-Event Systems |g 175 -- |g 5.3 |t Analysis of a Manufacturing System |g 176 -- |g 5.4 |t Load Balancing in a Computer Network |g 179 -- |g 6 |t Finite-Dimensional Dynamical Systems |g 185 -- |g 6.2 |t The Principal Stability and Boundedness Results for Ordinary Differential Equations |g 199 -- |g 6.3 |t The Principal Stability and Boundedness Results for Ordinary Difference Equations |g 211 -- |g 6.4 |t The Principal Stability and Boundedness Results for Discontinuous Dynamical Systems |g 219 -- |g 6.5 |t Converse Theorems for Ordinary Differential Equations |g 232 -- |g 6.6 |t Converse Theorems for Ordinary Difference Equations |g 241 -- |g 6.7 |t Converse Theorems for Finite-Dimensional DDS |g 243 -- |g 6.8 |t Appendix: Some Background Material on Differential Equations |g 245 -- |g 7 |t Finite-Dimensional Dynamical Systems: Specialized Results |g 255 -- |g 7.1 |t Autonomous and Periodic Systems |g 256 -- |g 7.2 |t Invariance Theory |g 258 -- |g 7.3 |t Domain of Attraction |g 263 -- |g 7.4 |t Linear Continuous-Time Systems |g 266 -- |g 7.5 |t Linear Discrete-Time Systems |g 285 -- |g 7.6 |t Perturbed Linear Systems |g 295 -- |g 7.7 |t Comparison Theory |g 316 -- |g 7.8 |t Appendix: Background Material on Differential Equations and Difference Equations |g 320 -- |g 8 |t Applications to Finite-Dimensional Dynamical Systems |g 337 -- |g 8.1 |t Absolute Stability of Regulator Systems |g 338 -- |g 8.2 |t Hopfield Neural Networks |g 344 -- |g 8.3 |t Digital Control Systems |g 353 -- |g 8.4 |t Pulse-Width-Modulated Feedback Control Systems |g 364 -- |g 8.5 |t Digital Filters |g 376 -- |g 9 |t Infinite-Dimensional Dynamical Systems |g 395 -- |g 9.2 |t The Principal Lyapunov Stability and Boundedness Results for Differential Equations in Banach Spaces |g 398 -- |g 9.3 |t Converse Theorems for Differential Equations in Banach Spaces |g 408 -- |g 9.4 |t Invariance Theory for Differential Equations in Banach Spaces |g 409 -- |g 9.5 |t Comparison Theory for Differential Equations in Banach Spaces |g 413 -- |g 9.6 |t Composite Systems |g 415 -- |g 9.7 |t Analysis of a Point Kinetics Model of a Multicore Nuclear Reactor |g 420 -- |g 9.8 |t Results for Retarded Functional Differential Equations |g 423 -- |g 9.9 |t Applications to a Class of Artificial Neural Networks with Time Delays |g 438 -- |g 9.10 |t Discontinuous Dynamical Systems Determined by Differential Equations in Banach Spaces |g 449 -- |g 9.11 |t Discontinuous Dynamical Systems Determined by Semigroups |g 463. |
| 520 | 1 | |a "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 systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model." "Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduating students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics."--Jacket. | |
| 538 | |a Mode of access: World Wide Web. | ||
| 588 | |a Machine converted from AACR2 source record. | ||
| 650 | 0 | |a Differentiable dynamical systems. |9 316677 | |
| 650 | 0 | |a Stability. |9 335125 | |
| 700 | 1 | |a Hou, Ling, |e author. | |
| 700 | 1 | |a Liu, Derong, |d 1963- |e author. |9 247759 | |
| 830 | 0 | |a Systems & control. |9 237623 | |
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