Lecture Notes in Control and Information Sciences

Linear Time-Varying Systems

Algebraic-Analytic Approach

Authors: Bourlès, Henri, Marinescu, Bogdan

  • 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
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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.

 

Reviews

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)

Table of contents (12 chapters)

  • Categories, Divisibility and Groups

    Bourlès, Henri (et al.)

    Pages 3-90

  • Rings and Modules

    Bourlès, Henri (et al.)

    Pages 91-187

  • Homological Algebra

    Bourlès, Henri (et al.)

    Pages 189-268

  • Galois Theory and Skew Polynomials

    Bourlès, Henri (et al.)

    Pages 269-308

  • Systems and Behaviors: A General Setting

    Bourlès, Henri (et al.)

    Pages 311-401

Buy this book

eBook $189.00
price for USA (gross)
  • ISBN 978-3-642-19727-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $239.00
price for USA
  • ISBN 978-3-642-19726-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Linear Time-Varying Systems
Book Subtitle
Algebraic-Analytic Approach
Authors
Series Title
Lecture Notes in Control and Information Sciences
Series Volume
410
Copyright
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-19727-7
DOI
10.1007/978-3-642-19727-7
Softcover ISBN
978-3-642-19726-0
Series ISSN
0170-8643
Edition Number
1
Number of Pages
XXVI, 638
Number of Illustrations and Tables
32 b/w illustrations
Topics