Communications and Control Engineering

Liapunov Functions and Stability in Control Theory

Authors: Bacciotti, Andrea, Rosier, Lionel

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About this book

This book presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control. Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs. In the 2nd edition of this successful book several new sections were added and old sections have been improved, e.g about the Zubovs method, Liapunov functions for discontinuous systems and cascaded systems. Many new examples, explanations and figures were added making this book accessible and well readable for engineers as well as mathematicians.

Reviews

Review in amazon:

Super Book December 16, 2002 P, Princeton:
Bacciotti and Rosier have managed to present a nonformal, yet rigorous and well-organized introduction to nonlinear stabilization and controllability. They have definetly captured the most important research trends in the area and have managed to cover a wide range of topics with appropriate deepness. My only suggestion would be to add a list of symbols to the book and to discuss Chow's Theorem and the accessibility rank condition. Thanks for a great book!

From the reviews of the second edition:

"This book has been written by famous scientists in the areas of stability and control theories. It presents a modern and self-contained treatment of the Lyapunov method for stability analysis in the framework of mathematical nonlinear control theory. … In the 2nd edition of this successful book several new sections have been added and old sections have been improved. A lot of new examples, explanations and figures are added making this book accessible and well readable for engineers as well as mathematicians." (Alexander O. Ignatyev, Zentralblatt MATH, Vol. 1078, 2006)


Table of contents (6 chapters)

Table of contents (6 chapters)
  • Differential equations

    Pages 1-17

  • Time invariant systems

    Pages 19-88

  • Time varying systems

    Pages 89-117

  • Differential inclusions

    Pages 119-165

  • Additional properties of strict Liapunov functions

    Pages 167-202

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-540-27397-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-3-540-21332-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.99
price for USA in USD
  • ISBN 978-3-642-05968-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Liapunov Functions and Stability in Control Theory
Authors
Series Title
Communications and Control Engineering
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-27397-4
DOI
10.1007/b139028
Hardcover ISBN
978-3-540-21332-1
Softcover ISBN
978-3-642-05968-1
Series ISSN
0178-5354
Edition Number
2
Number of Pages
XIII, 237
Additional Information
Originally published as volume 267 in the series "Lecture Notes Control" by Springer, London, 2001
Topics