Stability of Dynamical Systems

Continuous, Discontinuous, and Discrete Systems

  • 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-XII
  2. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 1-16
  3. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 17-70
  4. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 149-172
  5. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 173-183
  6. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 185-254
  7. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 255-336
  8. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 337-393
  9. Anthony N. Michel, Ling Hou, Derong Liu
    Pages 395-488
  10. Back Matter
    Pages 489-501

About this book

Introduction

In the analysis and synthesis of contemporary systems, engineers and scientists are frequently confronted with increasingly complex models that may simultaneously include components whose states evolve along continuous time and discrete instants; components whose descriptions may exhibit nonlinearities, time lags, transportation delays, hysteresis effects, and uncertainties in parameters; and components that cannot be described by various classical equations, as in the case of discrete-event systems, logic commands, and Petri nets. The qualitative analysis of such systems requires results for finite-dimensional and infinite-dimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics.

Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models described above. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model.

The book covers 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

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

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

Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems. The book may also serve as a self-study reference for graduate students, researchers, and practitioners in applied mathematics, engineering, computer science, physics, chemistry, biology, and economics.

Keywords

Lagrange and actor continuous continuous-time systems continuous-time systems digital signal processing discontinuous continuous-time systems discrete-time systems dynamical systems finite-dimensional systems hybrid systems infinite-dimensional systems system

Authors and affiliations

  • Anthony N. Michel
    • 1
  • Ling Hou
    • 2
  • Derong Liu
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Notre DameNotre DameU.S.A
  2. 2.Department of Electrical and Computer EngineeringSt. Cloud State UniversitySt. CloudU.S.A
  3. 3.Department of Electrical and Computer EngineeringUniversity of Illinois at ChicagoChicagoU.S.A

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4649-3
  • Copyright Information Birkhäuser Boston 2008
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4486-4
  • Online ISBN 978-0-8176-4649-3
  • About this book