Two-Dimensional Systems

From Introduction to State of the Art

  • Abdellah Benzaouia
  • Abdelaziz Hmamed
  • Fernando Tadeo

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 28)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 1-29
  3. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 31-58
  4. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 59-74
  5. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 75-109
  6. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 111-144
  7. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 145-165
  8. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 167-181
  9. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 183-221
  10. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 223-270
  11. Abdellah Benzaouia, Abdelaziz Hmamed, Fernando Tadeo
    Pages 271-292
  12. Back Matter
    Pages 293-295

About this book

Introduction

A solution permitting the stabilization of 2-dimensional (2-D) continuous-time saturated system under state feedback control is presented in this book. The problems of delay and saturation are treated at the same time. The authors obtain novel results on continuous 2-D systems using the unidirectional Lyapunov function. The control synthesis and the saturation and delay conditions are presented as linear matrix inequalities. Illustrative examples are worked through to show the effectiveness of the approach and many comparisons are made with existing results.

The second half of the book moves on to consider robust stabilization and filtering of 2-D systems with particular consideration being given to 2-D fuzzy systems. Solutions for the filter-design problems are demonstrated by computer simulation. The text builds up to the development of state feedback control for 2-D Takagi–Sugeno systems with stochastic perturbation. Conservatism is reduced by using slack matrices and the coupling between the Lyapunov matrix and the system matrices is broken by using basis-dependent Lyapunov functions. Mean-square asymptotic stability and prescribed H-infinity performance are guaranteed.

Two-Dimensional Systems emphasizes practical approaches to control and filter design under constraints that appear in real problems and uses off-the-shelf software to achieve its results. Researchers interested in control and filter design for multidimensional systems, especially multi-dimensional fuzzy systems, will find this book a useful resource as will graduate students specializing in dynamical sytems.

Keywords

Asymptotic Stability Delayed Continuous Systems Fornasini-Marchesini Models H-infinity Controller Design LMIs Linear Matrix Inequalities Multidimensional Systems Positive Systems Roesser Models Takagi–Sugeno Fuzzy Systems

Authors and affiliations

  • Abdellah Benzaouia
    • 1
  • Abdelaziz Hmamed
    • 2
  • Fernando Tadeo
    • 3
  1. 1.Department of PhysicsUniversity of Cadi AyyadMarrakechMorocco
  2. 2.Ecole Supérieure de TechnologieUniversity of Sidi Mohammed Ben AbdellahFèsMorocco
  3. 3.Departamento de Ingeniería de Sistemas y AutomáticaUniversity of ValladolidValladolidSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-20116-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-20115-3
  • Online ISBN 978-3-319-20116-0
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • About this book
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