Systems & Control: Foundations & Applications

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, pulse-width-modulated feedback control systems, and artificial neural networks
  • Real-world 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 self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics
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eBook $59.99
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  • ISBN 978-0-8176-4649-3
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  • ebooks can be used on all reading devices
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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 discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time 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, 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.

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 finite-dimensional dynamical systems

* Specialization of this stability theory to infinite-dimensional 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 self-study 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 self-contained 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)


Table of contents (9 chapters)

  • Introduction

    Michel, Anthony N. (et al.)

    Pages 1-16

  • Dynamical Systems

    Michel, Anthony N. (et al.)

    Pages 17-70

  • Fundamental Theory: The Principal Stability and Boundedness Results on Metric Spaces

    Michel, Anthony N. (et al.)

    Pages 71-148

  • Fundamental Theory:Specialized Stability and Boundedness Results on Metric Spaces

    Michel, Anthony N. (et al.)

    Pages 149-172

  • Applications to a Class of Discrete-Event Systems

    Michel, Anthony N. (et al.)

    Pages 173-183

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4649-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Stability of Dynamical Systems
Book Subtitle
Continuous, Discontinuous, and Discrete Systems
Authors
Series Title
Systems & Control: Foundations & Applications
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4649-3
DOI
10.1007/978-0-8176-4649-3
Series ISSN
2324-9749
Edition Number
1
Number of Pages
XII, 508
Number of Illustrations and Tables
44 b/w illustrations
Topics