Advertisement

© 2015

S-Variable Approach to LMI-Based Robust Control

  • Detailed account of the slack-variable approach to the increasingly popular study of linear-matrix-inequality-based control

  • Easily understandable exposition provides an entry path for non-experts to the latest control theory

  • Explicit description of LMI conditions enables readers to code them into programs in order to realise their effectiveness

  • Practical examples exemplify the guidelines on how to put theoretical LMI results into practice

Book

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 1-8
  3. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 9-59
  4. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 61-106
  5. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 107-137
  6. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 139-164
  7. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 165-198
  8. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 199-227
  9. Yoshio Ebihara, Dimitri Peaucelle, Denis Arzelier
    Pages 229-244
  10. Back Matter
    Pages 245-246

About this book

Introduction

This book shows how the use of S-variables (SVs) in enhancing the range of problems that can be addressed with the already-versatile linear matrix inequality (LMI) approach to control can, in many cases, be put on a more unified, methodical footing. Beginning with the fundamentals of the SV approach, the text shows how the basic idea can be used for each problem (and when it should not be employed at all). The specific adaptations of the method necessitated by each problem are also detailed. The problems dealt with in the book have the common traits that: analytic closed-form solutions are not available; and LMIs can be applied to produce numerical solutions with a certain amount of conservatism. Typical examples are robustness analysis of linear systems affected by parametric uncertainties and the synthesis of a linear controller satisfying multiple, often  conflicting, design specifications. For problems in which LMI methods produce conservative results, the SV approach is shown to achieve greater accuracy.

The authors emphasize the simplicity and easy comprehensibility of the SV approach and show how it can be implemented in programs without difficulty so that its power becomes readily apparent. The S-Variable Approach to LMI-Based Robust Control is a useful reference for academic control researchers, applied mathematicians and graduate students interested in LMI methods and convex optimization and will also be of considerable assistance to practising control engineers faced with problems of conservatism in their systems and controllers.

Keywords

LMI Linear Matriz Inequalities Linear Systems Analysis Linear Systems Synthesis Robustness Analysis Robustness Synthesis Slack Variable Approach Systems with Uncertainty

Authors and affiliations

  1. 1.Department of Electrical EngineeringKyoto UniversityKyotoJapan
  2. 2.Laboratory for Analysis and Architecture of Systems ScienceNational Centre for Scientific ResearchToulouseFrance
  3. 3.Laboratory for Analysis and Architecture of Systems ScienceNational Centre for Scientific ResearchToulouseFrance

About the authors

Yoshio Ebihara was born in Fukuoka, Japan on 12th May 1974. He received the D.E. degree in electrical engineering from Kyoto University in 2002. Since 2002 he has been in the Department of Electrical Engineering at Kyoto University where he was made an Associate Professor in 2010. He was the recipient of the 2002 American Control Conference Best Student Paper award and the SICE Annual Conference 2009 International Award.
Born in in Leningrad, 2nd March 1974, Dimitri Peaucelle received his PhD from the Paul Sabatier University, Toulouse, France in July 2000. He is now a CNRS researcher at the Laboratory for Analysis and Systems Architecture. He is currently a member of the IFAC Technical Committee on Robust Control, the head of the CNRS working group on methods and tools for robust analysis and control design and Scientific Secretary of the Scientific Council of the CNRS Information and Engineering Department. He was the organizer of the 2006 IFAC ROCOND Symposium and is the NOC Chair of the IFAC 2017 World Congress Steering Committee.

Bibliographic information

  • Book Title S-Variable Approach to LMI-Based Robust Control
  • Authors Yoshio Ebihara
    Dimitri Peaucelle
    Denis Arzelier
  • Series Title Communications and Control Engineering
  • Series Abbreviated Title Communicat., Control Engineering
  • DOI https://doi.org/10.1007/978-1-4471-6606-1
  • Copyright Information Springer-Verlag London 2015
  • Publisher Name Springer, London
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-1-4471-6605-4
  • Softcover ISBN 978-1-4471-7269-7
  • eBook ISBN 978-1-4471-6606-1
  • Series ISSN 0178-5354
  • Series E-ISSN 2197-7119
  • Edition Number 1
  • Number of Pages XVII, 246
  • Number of Illustrations 4 b/w illustrations, 34 illustrations in colour
  • Topics Control and Systems Theory
    Systems Theory, Control
    Optimization
  • Buy this book on publisher's site
Industry Sectors
Automotive
Chemical Manufacturing
Biotechnology
Electronics
IT & Software
Telecommunications
Aerospace
Pharma
Materials & Steel
Oil, Gas & Geosciences
Engineering