Fractional Order Differentiation and Robust Control Design

CRONE, H-infinity and Motion Control

  • Jocelyn Sabatier
  • Patrick Lanusse
  • Pierre Melchior
  • Alain Oustaloup

Table of contents

  1. Front Matter
    Pages i-ix
  2. J. Sabatier, C. Farges, A. Oustaloup
    Pages 1-61
  3. P. Lanusse, J. Sabatier, A. Oustaloup
    Pages 63-105
  4. P. Lanusse, J. Sabatier, D. Nelson Gruel, A. Oustaloup
    Pages 107-192
  5. J. Sabatier, C. Farges, L. Fadiga
    Pages 193-235

About this book


This monograph collates the past decade’s work on fractional models and fractional systems in the fields of analysis, robust control and path tracking. Themes such as PID control, robust path tracking design and motion control methodologies involving fractional differentiation are amongst those explored. It juxtaposes recent theoretical results at the forefront in the field, and applications that can be used as exercises that will help the reader to assimilate the proposed methodologies.

The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and “real state”, tackling the problem of fractional model initialization.

Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity control to fractional models. An exhaustive description of the three generations of CRONE is also provided, along with several useful academic examples, treated with the CRONE control Matlab toolbox, which illustrate the various control strategies.

Since prefilters are additional but often under-studied degrees of freedom to tune a control loop, the last part of this book presents three different approaches: fractional prefilter, input shaping and flatness principles that have been extended to fractional models. All these approaches are applied to experimental closed loop systems.


CRONE Control and Robust Control Fractional PI Fractional Systems Linear Matrix Inequalities PID Controllers Path Planning Path Tracking

Authors and affiliations

  • Jocelyn Sabatier
    • 1
  • Patrick Lanusse
    • 2
  • Pierre Melchior
    • 3
  • Alain Oustaloup
    • 4
  1. 1.LAPS - Bat A4IMS Laboratory - CNRS UMR 5218 –Bordeaux INP – Bordeaux UniversityTalenceFrance
  2. 2.LAPS - Bat A4IMS Laboratory - CNRS UMR 5218 –Bordeaux INP – Bordeaux UniversityTalenceFrance
  3. 3.Universite Bordeaux 1-IPB/Enseirb-Matmec LAPS - Bat A4IMS Laboratory - CNRS UMR 5218 –Bordeaux INP – Bordeaux UniversityTalenceFrance
  4. 4.IMS Laboratory LAPS - Bat A4IMS Laboratory - CNRS UMR 5218 –Bordeaux INP – Bordeaux UniversityTalenceFrance

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media Dordrecht 2015
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-94-017-9806-8
  • Online ISBN 978-94-017-9807-5
  • Series Print ISSN 2213-8986
  • Series Online ISSN 2213-8994
  • Buy this book on publisher's site