Cover image for Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

Author Pierre Borne , Mohammed Chadli
Release Date: 2012/11/01
ISBN: 9781118577226
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Book Description

Much work on analysis and synthesis problems relating to the multiple model approach has already been undertaken. This has been motivated by the desire to establish the problems of control law synthesis and full state estimation in numerical terms.

In recent years, a general approach based on multiple LTI models (linear or affine) around various function points has been proposed. This so-called multiple model approach is a convex polytopic representation, which can be obtained either directly from a nonlinear mathematical model, through mathematical transformation or through linearization around various function points.

This book concentrates on the analysis of the stability and synthesis of control laws and observations for multiple models. The authors' approach is essentially based on Lyapunov's second method and LMI formulation. Uncertain multiple models with unknown inputs are studied and quadratic and non-quadratic Lyapunov functions are also considered.

Table of Contents

  1. Cover
  2. Contents
  3. Title page
  4. Copyright page
  5. Notations
  6. Introduction
  7. Chapter 1: Multiple Model Representation
    1. 1.1. Introduction
    2. 1.2. Techniques for obtaining multiple models
    3. 1.3. Analysis and synthesis tools
  8. Chapter 2: Stability of Continuous Multiple Models
    1. 2.1. Introduction
    2. 2.2. Stability analysis
    3. 2.3. Relaxed stability
    4. 2.4. Example
    5. 2.5. Robust stability
    6. 2.6. Conclusion
  9. Chapter 3: Multiple Model State Estimation
    1. 3.1. Introduction
    2. 3.2. Synthesis of multiple observers
    3. 3.3. Multiple observer for an uncertain multiple model
    4. 3.4. Synthesis of unknown input observers
    5. 3.5. Synthesis of unknown input observers: another approach
    6. 3.6. Conclusion
  10. Chapter 4: Stabilization of Multiple Models
    1. 4.1. Introduction
    2. 4.2. Full state feedback control
    3. 4.3. Observer-based controller
    4. 4.4. Static output feedback control
    5. 4.5. Conclusion
  11. Chapter 5: Robust Stabilization of Multiple Models
    1. 5.1. Introduction
    2. 5.2. State feedback control
    3. 5.3. Output feedback control
    4. 5.4. Observer-based control
    5. 5.5. Conclusion
  12. Conclusion
  13. APPENDICES
    1. Appendix 1: LMI Regions
      1. A1.1. Definition of an LMI region
      2. A1.2. Interesting LMI region examples
    2. Appendix 2: Properties of M-Matrices
    3. Appendix 3: Stability and Comparison Systems
      1. A3.1. Vector norms and overvaluing systems
      2. A3.2. Vector norms and the principle of comparison
      3. A3.3. Application to stability analysis
  14. Bibliography
  15. Index
52.14.130.13