Happy Holidays! Over 120,000 eBooks at just 19.99 each— Pick a favorite today

Systems & Control: Foundations & Applications

Stability of Dynamical Systems

On the Role of Monotonic and Non-Monotonic Lyapunov Functions

Authors: Michel, Anthony N., Hou, Ling, Liu, Derong

  • Second edition of the first unified book covering the analysis of all the major types of dynamical systems models
  • Exercises and minimal prerequisites make the work suitable as a textbook for graduate courses in stability theory of dynamical systems
  • Real-world applications to manufacturing, computer load balancing problems, and many more
see more benefits

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-15275-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-15274-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 18, 2016
  • ISBN 978-3-319-33080-8
  • Free shipping for individuals worldwide
About this Textbook

The second edition of this textbook  provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.  For these system models, it presents results which comprise the classical Lyapunov stability theory involving monotonic Lyapunov functions, as well as corresponding contemporary stability results involving non-monotonic Lyapunov functions.  Specific examples from several diverse areas are given to demonstrate the applicability of the developed theory to many important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, and artificial neural networks.

 The authors cover 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 involving monotonic and non-monotonic Lyapunov functions

- Specialization of this stability theory to finite-dimensional dynamical systems

- Specialization of this stability theory to infinite-dimensional dynamical systems

Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in stability theory of dynamical systems.  It may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, economics, and the physical and life sciences.

Review of the First Edition:

“The authors have done an excellent job maintaining the rigor of the presentation, and in providing standalone statements for diverse types of systems.  [This] is a very interesting book which complements the existing literature. [It] is clearly written, and difficult concepts are illustrated by means of good examples.”

- Alessandro Astolfi, IEEE Control Systems Magazine, February 2009

About the authors

Anthony N. Michel, PhD, is Professor Emeritus in the College of Engineering at the University of Notre Dame.

Ling Hou, PhD, is Professor in the Department of Electrical and Computer Engineering at St. Cloud State University.

Derong Liu, PhD, is Professor in the Department of Electrical and Computer Engineering at the University of Illinois at Chicago.

Reviews

“This new edition of the book by Michel, Hou, and Liu provides a scholarly and comprehensive view of Lyapunov stability that should be accessible to mathematically inclined graduate students and to many researchers in the control field. It is a welcome addition to the published literature.” (N. Harris McClamroch, IEEE Control Systems Magazine, Vol. 36 (1), February, 2016)

“This text have provided comprehensive sources for the materials and results on stability theory of all the dynamical systems … . The book also contains numerous problems and suggestions for further study at the end of the main chapters. … book will provide an excellent source of materials for graduate students studying the stability theory of dynamical systems, and for self-study by researchers and practitioners interested in the systems theory of engineering, physics, computer science, chemistry, life science, and economics.” (Olusola Akinyele, Mathematical Reviews, November, 2015)


Table of contents (9 chapters)

  • Introduction

    Michel, Anthony N. (et al.)

    Pages 1-18

  • Dynamical Systems

    Michel, Anthony N. (et al.)

    Pages 19-76

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

    Michel, Anthony N. (et al.)

    Pages 77-197

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

    Michel, Anthony N. (et al.)

    Pages 199-224

  • Applications to a Class of Discrete-Event Systems

    Michel, Anthony N. (et al.)

    Pages 225-236

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-15275-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-319-15274-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: November 18, 2016
  • ISBN 978-3-319-33080-8
  • Free shipping for individuals worldwide
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Stability of Dynamical Systems
Book Subtitle
On the Role of Monotonic and Non-Monotonic Lyapunov Functions
Authors
Series Title
Systems & Control: Foundations & Applications
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-15275-2
DOI
10.1007/978-3-319-15275-2
Hardcover ISBN
978-3-319-15274-5
Softcover ISBN
978-3-319-33080-8
Series ISSN
2324-9749
Edition Number
2
Number of Pages
XVIII, 653
Number of Illustrations and Tables
46 b/w illustrations, 14 illustrations in colour
Topics