Stability of Dynamical Systems
Continuous, Discontinuous, and Discrete Systems
Authors: Michel, Anthony N., Hou, Ling, Liu, Derong
 First unified book covering the analysis of all the major types of dynamical systems models
 Many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulsewidthmodulated feedback control systems, and artificial neural networks
 Realworld applications to manufacturing and computer load balancing problems
 Exercises and minimal prerequisites make the work suitable as a textbook for graduate courses in stability theory of dynamical systems
 The book may also be used as a selfstudy reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics
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 About this Textbook

In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discreteevent systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finitedimensional and infinitedimensional systems; continuoustime and discretetime systems; continuous continuoustime and discontinuous continuoustime systems; and hybrid systems involving a mixture of continuous and discrete dynamics.
Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. 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, pulsewidthmodulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discreteevent systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model.
The book covers the following four general topics:
* Representation and modeling of dynamical systems of the types described above
* Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces
* Specialization of this stability theory to finitedimensional dynamical systems
* Specialization of this stability theory to infinitedimensional dynamical systems
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 selfstudy reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.
 Reviews

From the reviews:
"The book under review provides a single comprehensive source for the materials and results on stability analysis of all the dynamical systems … . contains numerous problems and suggestions for further study at the end of the main chapters. This book will be an excellent source of material for beginning graduate students studying the stability theory of dynamical systems and for self study by researchers and practitioners interested in systems theory of engineering, computer science, chemistry, life sciences and economics." (Olusola Akinyele, Mathematical Reviews, Issue 2008 i)
"The goal of this book is to provide a reference text for graduate students and researchers on stability theory for the class of systems encountered in modern applications. In this respect, the goal is indeed achieved since the book offers a selfcontained presentation of stability theory.
…[In chapter 2] special care is taken to highlight the key concepts and ingredients, and an effort is made to consider all classes of systems that are relevant to applications. In addition, several important issues illustrating properties of solutions are highlighted by means of elementary, yet carefully selected, examples…The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems…[Chapters 6, 7, and 8] contain several nonstandard results and examples, thus making interesting reading even for experts.
…The use of this book as a reference text in stability theory is facilitated by an extensive index…In conclusion, Stability of Dynamical Systems: Continuous, Discontinuous, and Discrete Systems is a very interesting book, which complements the existing literature. The book is clearly written, and difficult concepts are illustrated by means of good examples. The book is suitable for readers with a solid mathematical background as well as some basic systems and control knowledge. The book should provide a useful reference for researchers working in control theory as well as for Ph.D. students." (Alessandro Astolfi, IEEE Control Systems Magazine, February 2009)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Stability of Dynamical Systems
 Book Subtitle
 Continuous, Discontinuous, and Discrete Systems
 Authors

 Anthony N. Michel
 Ling Hou
 Derong Liu
 Series Title
 Systems & Control: Foundations & Applications
 Copyright
 2008
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9780817646493
 DOI
 10.1007/9780817646493
 Series ISSN
 23249749
 Edition Number
 1
 Number of Pages
 XII, 508
 Number of Illustrations and Tables
 44 b/w illustrations
 Topics