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Saturated Control of Linear Systems

  • Abdellah Benzaouia
  • Fouad Mesquine
  • Mohamed Benhayoun
Book

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 124)

Table of contents

  1. Front Matter
    Pages i-xxxvii
  2. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 1-22
  3. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 23-42
  4. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 43-68
  5. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 69-84
  6. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 85-104
  7. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 105-125
  8. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 127-143
  9. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 145-168
  10. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 169-186
  11. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 187-199
  12. Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun
    Pages 201-222
  13. Back Matter
    Pages 223-226

About this book

Introduction

This book deals with a combination of two main problems for the first time. They are saturation on control and on the rate (or increment) of the control, and the solution of unsymmetrical saturation on the control by LMIs. It treats linear systems in state space form, in both the continuous- and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate, such that the system evolves respecting incremental or rate constraints if any. A pole assignment technique is then used to solve the problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on control alone or on both control and its increment or rate. Illustrative examples show the application of these methods on academic examples or on such real plant models as the double integrator system. This problem is then extended to various others including:

  • systems with constraints and perturbations;
  • singular systems with constrained control;
  • systems with unsymmetrical saturations; 
  • saturated systems with delay, and
  • 2-D systems with saturations.

The solutions obtained are of two types:

  • necessary and sufficient conditions solved with linear programming techniques; and
  • sufficient conditions under LMIs.

A new approach extends existing techniques for dealing with symmetrical saturations to take direct account of unsymmetrical saturations into account with LMIs. This tool enables the authors to obtain new results on continuous- and discrete-time systems. The book uses illustrative examples and figures and provides many comparisons with existing results.

Systems theoreticians interested in multidimensional systems and practitioners working with saturated and constrained controllers will find the research and background presented in Saturated Control of Linear Systemsi> to be of considerable interest in helping them overcome problems with their plant and in stimulating further research.

Keywords

Constrained Control Asymmetric Saturation Singular Linear Systems Constrained Observers Positive Invariance LMI Linear Matrix Inequality 2-dimensional Systems Delayed Systems

Authors and affiliations

  • Abdellah Benzaouia
    • 1
  • Fouad Mesquine
    • 2
  • Mohamed Benhayoun
    • 3
  1. 1.Department of Physics, Faculty of Science SemlaliaUniversity Cadi AyyadMarrakechMorocco
  2. 2.Department of Physics, Faculty of Science SemlaliaUniversity Cadi AyyadMarrakechMorocco
  3. 3.Department of Physics, Faculty of Science SemlaliaUniversity Cadi AyyadMarrakechMorocco

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-65990-9
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-65989-3
  • Online ISBN 978-3-319-65990-9
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • Buy this book on publisher's site