Liapunov Functions and Stability in Control Theory

  • Andrea Bacciotti
  • Lionel Rosier

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


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.


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

Authors and affiliations

  • Andrea Bacciotti
    • 1
  • Lionel Rosier
    • 2
  1. 1.Dipto. MatematicaPolitecnico TorinoTorinoItaly
  2. 2.Institut Elie CartanUniversité Nancy 1Vandoeuvre-lès-Nancy CedexFrance

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-540-21332-1
  • Online ISBN 978-3-540-27397-4
  • Series Print ISSN 0178-5354
  • Buy this book on publisher's site