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Multiple Models Approach in Automation : Takagi-Sugeno Fuzzy Systems,9781848214125
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Multiple Models Approach in Automation : Takagi-Sugeno Fuzzy Systems

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In recent decades, many studies on the analysis and synthesis of problems have been devoted to nonlinear systems using polytopic representation. Such an approach includes differential inclusions, Takagi-Sugeno fuzzy models and multi-model approach. This choice was motivated by the desire to formulate synthesis problems on a numerical tools base. Then controllers and observers are designed based on LMI (Linear matrix Inequalities) and Lyapunov functions. Different control laws (state feedback, output feedback) and observers (linear observer, unknown input observers) are studied taking into account uncertainties.

Table of Contents

General Introduction

Chapter 1 : Multiple Model representation

1.1 Introduction  

1.2 How to get Multiple Model  

1.3 Analysis and Synthesis tools

1.3.1 Lyapunov method

1.3.2 Numerical tools : Linear Matrix Inequalities

1.3.3 Different control laws

Chapter 2 : Stability of  Multiple Model

2.1 Introduction  

2.2 Stability analysis 

2.3 Relaxed stability  

2.4 Example

2.5 Robust stability  

2.6 Conclusion  

Chapter 3 : Observers design

3.1 Introduction  

3.2 Basic synthesis conditions 

3.3 Observer for uncertain Multiple Model  

3.4 Design of unknown inputs observer  

3.5 Design of sliding mode observer

3.6 Conclusion  

Chapter 4 : Controllers design

4.1 Introduction  

4.2 State feedback controller 

4.3 Observer-based controller

4.4 Static output feedback controller

4.5 Conclusion  

Chapter 5 : Robust stabilization of Multiple Model

5.1 Introduction  

5.2 State feedback controller

5.2.1 Norm bounded uncertainties

5.2.2 Interval uncertainties

5.3 Static output feedback controller

5.3.1 Norm bounded uncertainties

5.3.2 Interval uncertainties

5.4 Dynamic output feedback controller

5.5 Conclusion

General conclusion


Annexe 1 –  Regions

Annexe 2 – M matrices properties


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