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Stability and Stabilization of Linear Systems with Saturating Actuators

  • Book
  • © 2011

Overview

Authors:
  1. Sophie Tarbouriech

    1. Labo. Analyse et Architecture des, Systèmes (LAAS), CNRS, Toulouse CX 4, France

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  2. Germain Garcia

    1. Groupe CSC, CNRS - LAAS, Toulouse CX, France

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  3. João Manoel Gomes da Silva Jr.

    1. Departamento de Engenharia Elétrica, Universidade Federal do Rio Grande do Su, Porto Alegre, Brazil

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  4. Isabelle Queinnec

    1. Lab. Analyse et Archit. des Syst. (LAAS), CNRS, Toulouse CX 4, France

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  • Gives the reader an in-depth understanding of the phenomena caused by the more-or-less ubiquitous problem of actuator saturation.
  • Proposes methods and algorithms designed to avoid, manage or overcome the effects of actuator saturation.
  • Uses a state-space approach to ensure local and global stability of the systems considered.
  • Compilation of fifteen years’ worth of research results.
  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XXI
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  2. Generalities

    1. Front Matter

      Pages 1-1
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    2. Linear Systems Subject to Control Saturation—Problems and Modeling

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 3-48

  3. Stability Analysis and Stabilization

    1. Front Matter

      Pages 49-49
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  4. Stability analysis and stabilization

    1. Stability Analysis and Stabilization—Polytopic Representation Approach

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 51-121

    2. Stability Analysis and Stabilization—Sector Nonlinearity Model Approach

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 123-183

    3. Analysis via the Regions of Saturation Model

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 185-208

    4. Synthesis via a Parameterized ARE Approach or a Parameterized LMI Approach

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 209-264

  5. Anti-windup

    1. Front Matter

      Pages 265-265
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    2. An Overview of Anti-windup Techniques

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 267-281

    3. Anti-windup Compensator Synthesis

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 283-309

    4. Applications of Anti-windup Techniques

      • Sophie Tarbouriech, Germain Garcia, João Manoel Gomes da Silva Jr., Isabelle Queinnec
      Pages 311-352

  6. Back Matter

    Pages 353-430
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Keywords

About this book

This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.

Reviews

From the reviews:

“This monograph covers a wide range of topics in the problems of stability and stabilization for linear control systems in the presence of actuator saturation. … The book will be useful to researchers and graduate students in various areas of control applications concerning systems with saturation.” (Vladimir Sobolev, zbMATH, Vol. 1279, 2014)

“This nice book brings together the results of many years of research efforts by the authors and others about the control of linear systems with saturating actuators. … This book can be useful for students, researchers and control engineers facing practical problems.” (Paulo Sérgio Pereira da Silva, Mathematical Reviews, December, 2013)

Authors and Affiliations

  • Labo. Analyse et Architecture des, Systèmes (LAAS), CNRS, Toulouse CX 4, France

    Sophie Tarbouriech

  • Groupe CSC, CNRS - LAAS, Toulouse CX, France

    Germain Garcia

  • Departamento de Engenharia Elétrica, Universidade Federal do Rio Grande do Su, Porto Alegre, Brazil

    João Manoel Gomes da Silva Jr.

  • Lab. Analyse et Archit. des Syst. (LAAS), CNRS, Toulouse CX 4, France

    Isabelle Queinnec

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