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Advanced Takagi‒Sugeno Fuzzy Systems

Delay and Saturation

  • Abdellah Benzaouia
  • Ahmed El Hajjaji

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 8)

Table of contents

  1. Front Matter
    Pages i-xxxii
  2. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 1-40
  3. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 41-83
  4. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 85-110
  5. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 111-125
  6. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 127-149
  7. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 151-167
  8. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 169-207
  9. Abdellah Benzaouia, Ahmed El Hajjaji
    Pages 251-288
  10. Back Matter
    Pages 289-294

About this book

Introduction

This monograph puts the reader in touch with a decade’s worth of new developments in the field of fuzzy control specifically those of the popular Takagi-Sugeno (T-S) type. New techniques for stabilizing control analysis and design based on multiple Lyapunov functions and linear matrix inequalities (LMIs), are proposed. All the results are illustrated with numerical examples and figures and a rich bibliography is provided for further investigation.

Control saturations are taken into account within the fuzzy model. The concept of positive invariance is used to obtain sufficient asymptotic stability conditions for the fuzzy system with constrained control inside a subset of the state space.

The authors also consider the non-negativity of the states. This is of practical importance in many chemical, physical and biological processes that involve quantities that have intrinsically constant and non-negative sign: concentration of substances, level of liquids, etc. Results for linear systems are then extended to linear systems with delay. It is shown that LMI techniques can usually handle the new constraint of non-negativity of the states when care is taken to use an adequate Lyapunov function. From these foundations, the following further problems are also treated:

·        asymptotic stabilization of uncertain T-S fuzzy systems with time-varying delay, focusing on delay-dependent stabilization synthesis based on parallel distributed controller (PDC);

·        asymptotic stabilization of uncertain T-S fuzzy systems with multiple delays, focusing on delay-dependent stabilization synthesis based on PDC with results obtained under linear programming;

·        design of delay-independent, observer-based, H-infinity control for T–S fuzzy systems with time varying delay; and

·        asymptotic stabilization of 2-D T–S fuzzy systems.

Advanced Takagi–Sugeno Fuzzy Systems provides researchers and graduate students interested in fuzzy control systems with further approaches based LMI and LP.

Keywords

Delayed Systems Fuzzy Control Observer-based Fuzzy Control Positive Systems Reliable Control Saturated Control Takagi‒Sugeno Systems

Authors and affiliations

  • Abdellah Benzaouia
    • 1
  • Ahmed El Hajjaji
    • 2
  1. 1.Department of PhysicsUniversity of Cadi AyyadMarrakechMorocco
  2. 2.Laboratoire de Modélisation, Information et SystèmesUniversité de Picardie Jules VerneAmiensFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05639-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-05638-8
  • Online ISBN 978-3-319-05639-5
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • Buy this book on publisher's site
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