Stability of Dynamical Systems

On the Role of Monotonic and Non-Monotonic Lyapunov Functions

  • Anthony N. Michel
  • Ling Hou
  • Derong Liu

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 1-18
  3. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 19-76
  4. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 199-224
  5. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 225-236
  6. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 237-337
  7. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 339-457
  8. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 459-538
  9. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 539-642
  10. Back Matter
    Pages 643-653

About this book


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-monotonicLyapunov 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 bookcan 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


Lyapunov stability boundedness of motions continuous-time dynamical system difference equations differential equations in Banach spaces discontinuous dynamical system discrete-time dynamical system dynamical system equilibrium point finite-dimensional dynamical system functional differential equations infinite-dimensional dynamical system invariance theory ordinary differential equations partial differential equations semigroups

Authors and affiliations

  • Anthony N. Michel
    • 1
  • Ling Hou
    • 2
  • Derong Liu
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  2. 2.St. Cloud State University Dept. Electrical & Computer EngineeringSt. CloudUSA
  3. 3.Department of Electrical and Computer EngineeringUniversity of Illinois at ChicagoChicagoUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-15274-5
  • Online ISBN 978-3-319-15275-2
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site