S-Variable Approach to LMI-Based Robust Control

  • Yoshio Ebihara
  • Dimitri Peaucelle
  • Denis Arzelier

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

  • Yoshio Ebihara
    • 1
  • Dimitri Peaucelle
    • 2
  • Denis Arzelier
    • 3
  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

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-6606-1
  • Copyright Information Springer-Verlag London 2015
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-4471-6605-4
  • Online ISBN 978-1-4471-6606-1
  • Series Print ISSN 0178-5354
  • Series Online ISSN 2197-7119
  • About this book
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