Switching in Systems and Control

  • Daniel Liberzon

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Daniel Liberzon
      Pages 3-15
  3. Stability of Switched Systems

    1. Front Matter
      Pages 17-20
    2. Daniel Liberzon
      Pages 21-51
    3. Daniel Liberzon
      Pages 53-71
  4. Switching Control

    1. Front Matter
      Pages 73-76
    2. Daniel Liberzon
      Pages 93-128
    3. Daniel Liberzon
      Pages 129-165
  5. Back Matter
    Pages 167-233

About this book


This book examines switched systems from a control-theoretic perspective, focusing on stability analysis and control synthesis of systems that combine continuous dynamics with switching events. The theory of such switched systems is related to the study of hybrid systems, which has recently attracted considerable attention among control theorists, computer scientists, and practicing engineers. Aimed at readers with a background in systems and control, this book bridges the gap between classical mathematical control theory and the interdisciplinary field of hybrid systems.

The book is divided into three main parts:

* Part I introduces the classes of systems studied in the book

* Part II develops stability theory for switched systems; it covers single and multiple Lyapunov function analysis methods, Lie-algebraic stability criteria, stability under limited-rate switching, and switched systems with various types of useful special structures

* Part III is devoted to switching control design; it describes several wide classes of continuous-time control systems for which the logic-based switching paradigm emerges naturally as a control design tool. Switching control algorithms for several specific problems are discussed.

The text adopts a progressive approach, presenting elementary concepts informally and more advanced topics with greater rigor. Results are first derived for linear systems and then extended to nonlinear systems.  Full proofs for most results are provided. An extensive bibliography and a section of technical and historical notes complete the work.

Requiring only familiarity with the basic theory of linear systems, the book is suitable as a text for a graduate course on switched systems and switching control.  It may also serve as an introduction to this active area of research for control theorists and mathematicians, as well as a useful reference for experts in the field.


Algebra Lie-Algebra Nonlinear system algorithm algorithms control control system control theory feedback linear optimization modeling sensor stability stability theory uncertainty

Authors and affiliations

  • Daniel Liberzon
    • 1
  1. 1.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2003
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6574-0
  • Online ISBN 978-1-4612-0017-8
  • Series Print ISSN 2324-9749
  • Buy this book on publisher's site