© 2011

Linear Time-Varying Systems

Algebraic-Analytic Approach

  • Comprehensive treatment of the theory of linear time-varying systems

  • Unified approach based on ring and module theory

  • Written by leading experts in this field


Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 410)

Table of contents

  1. Front Matter
  2. Mathematical Tools

    1. Front Matter
      Pages 1-1
    2. Henri Bourlès, Bogdan Marinescu
      Pages 3-90
    3. Henri Bourlès, Bogdan Marinescu
      Pages 91-187
    4. Henri Bourlès, Bogdan Marinescu
      Pages 189-268
    5. Henri Bourlès, Bogdan Marinescu
      Pages 269-308
  3. Algebraic Theory of Linear Systems

    1. Front Matter
      Pages 309-309
    2. Henri Bourlès, Bogdan Marinescu
      Pages 311-401
    3. Henri Bourlès, Bogdan Marinescu
      Pages 403-452
    4. Henri Bourlès, Bogdan Marinescu
      Pages 453-496
  4. Applications

    1. Front Matter
      Pages 497-497
    2. Henri Bourlès, Bogdan Marinescu
      Pages 499-514
    3. Henri Bourlès, Bogdan Marinescu
      Pages 515-522
    4. Henri Bourlès, Bogdan Marinescu
      Pages 523-543
    5. Henri Bourlès, Bogdan Marinescu
      Pages 545-580
  5. Complements

    1. Front Matter
      Pages 581-581
    2. Henri Bourlès, Bogdan Marinescu
      Pages 583-603
  6. Back Matter

About this book


The aim of this book is to propose a new approach to analysis and control of linear time-varying systems.  These systems are defined in an intrinsic way, i.e., not by a particular representation (e.g., a transfer matrix or a state-space form) but as they are actually.  The system equations, derived, e.g., from the laws of physics, are gathered to form an intrinsic mathematical object, namely a finitely presented module over a ring of operators.  This is strongly connected with the engineering point of view, according to which a system is not a specific set of equations but an object of the material world which can be described by equivalent sets of equations.  This viewpoint makes it possible to formulate and solve efficiently several key problems of the theory of control in the case of linear time-varying systems.  The solutions are based on algebraic analysis.


This book, written for engineers, is also useful for mathematicians since it shows how algebraic analysis can be applied to solve engineering problems.


Henri Bourlès is a Professor and holds the industrial automation chair at the Conservatoire national des arts et métiers in France. He has been teaching automation for over 20 years in engineering and graduate schools.


Bogdan Marinescu is currently research engineer at the French Transmission System Operator (RTE) and Associate Professor at SATIE-Ecole Normale Supérieure de Cachan.



LTV System Linear Time Varying Systems Module Theory Structure at Infinity

Authors and affiliations

  1. 1.SATIE, CNAM/ENS de CachanCachanFrance
  2. 2.RTE EDF TransportVersaillesFrance

Bibliographic information

  • Book Title Linear Time-Varying Systems
  • Book Subtitle Algebraic-Analytic Approach
  • Authors Henri Bourlès
    Bogdan Marinescu
  • Series Title Lecture Notes in Control and Information Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Softcover ISBN 978-3-642-19726-0
  • eBook ISBN 978-3-642-19727-7
  • Series ISSN 0170-8643
  • Series E-ISSN 1610-7411
  • Edition Number 1
  • Number of Pages XXVI, 638
  • Number of Illustrations 32 b/w illustrations, 0 illustrations in colour
  • Topics Control, Robotics, Mechatronics
    Systems Theory, Control
  • Buy this book on publisher's site
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From the reviews:

“This nice book introduces an algebraic-analytic approach for studying linear time-varying (LTV) systems. … may be useful for anyone interested in algebraic approaches of systems theory. … Non-mathematicians will find a clear and well-written presentation of the mathematical background in the first part of this book, which certainly increases its readability. The material of the second and third parts is also interesting for mathematicians, who will find a precise presentation of applications of these algebraic methods to systems theory.” (Paulo Sérgio Pereira da Silva, Mathematical Reviews, Issue 2012 c)