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© 2005

Liapunov Functions and Stability in Control Theory

Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Pages 89-117
  3. Pages 119-165
  4. Back Matter
    Pages 219-237

About this book

Introduction

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.

Keywords

Differential Inclusions Direct Liapunov Method Nonlinear Systems automatic control control control theory nonlinear control nonlinear system stability stabilization

Authors and affiliations

  1. 1.Dipto. MatematicaPolitecnico TorinoTorinoItaly
  2. 2.Institut Elie CartanUniversité Nancy 1Vandoeuvre-lès-Nancy CedexFrance

Bibliographic information

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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)