Stability and Boundary Stabilization of 1-D Hyperbolic Systems

  • Georges Bastin
  • Jean-Michel Coron

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 88)

Also part of the PNLDE Subseries in Control book sub series (PNLDE-SC, volume 88)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Georges Bastin, Jean-Michel Coron
    Pages 1-54
  3. Georges Bastin, Jean-Michel Coron
    Pages 55-83
  4. Georges Bastin, Jean-Michel Coron
    Pages 85-116
  5. Georges Bastin, Jean-Michel Coron
    Pages 117-158
  6. Georges Bastin, Jean-Michel Coron
    Pages 159-201
  7. Georges Bastin, Jean-Michel Coron
    Pages 203-218
  8. Georges Bastin, Jean-Michel Coron
    Pages 219-228
  9. Georges Bastin, Jean-Michel Coron
    Pages 229-241
  10. Back Matter
    Pages 243-307

About this book


This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations.  It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them.  With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices.

The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis.  Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones.  They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs.  The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in practical applications of boundary feedback control. 

Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering.  The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.


Dissipativity Hyperbolic Systems Linear Systems of Conservation Laws Linear and Nonlinear Balance Laws Nonlinear Partial Differential Equations Nonlinear Systems of Conservation Laws

Authors and affiliations

  • Georges Bastin
    • 1
  • Jean-Michel Coron
    • 2
  1. 1.Mathematical Engineering, ICTEAMUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Laboratoire Jacques-Louis Lions Boîte courrier 187Université Pierre et Marie CurieParis Cedex 05France

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-32060-1
  • Online ISBN 978-3-319-32062-5
  • Series Print ISSN 1421-1750
  • Series Online ISSN 2374-0280
  • Buy this book on publisher's site