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E-raamat: Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

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  • Formaat: EPUB+DRM
  • Ilmumisaeg: 14-Dec-2012
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118577226
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Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy SystemsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 14-Dec-2012
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118577226
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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.

Notations ix
Introduction xiii
Chapter 1 Multiple Model Representation
1(40)
1.1 Introduction
1(1)
1.2 Techniques for obtaining multiple models
2(27)
1.2.1 Construction of multiple models by identification
3(5)
1.2.2 Multiple model construction by linearization
8(6)
1.2.3 Multiple model construction by mathematical transformation
14(8)
1.2.4 Multiple model representation using the neural approach
22(7)
1.3 Analysis and synthesis tools
29(12)
1.3.1 Lyapunov approach
29(2)
1.3.2 Numeric tools: linear matrix inequalities
31(7)
1.3.3 Multiple model control techniques
38(3)
Chapter 2 Stability of Continuous Multiple Models
41(24)
2.1 Introduction
41(1)
2.2 Stability analysis
42(7)
2.2.1 Exponential stability
48(1)
2.3 Relaxed stability
49(3)
2.4 Example
52(2)
2.5 Robust stability
54(9)
2.5.1 Norm-bounded uncertainties
56(1)
2.5.2 Structured parametric uncertainties
57(3)
2.5.3 Analysis of nominal stability
60(2)
2.5.4 Analysis of robust stability
62(1)
2.6 Conclusion
63(2)
Chapter 3 Multiple Model State Estimation
65(34)
3.1 Introduction
65(2)
3.2 Synthesis of multiple observers
67(10)
3.2.1 Linearization
68(2)
3.2.2 Pole placement
70(2)
3.2.3 Application: asynchronous machine
72(3)
3.2.4 Synthesis of multiple observers
75(2)
3.3 Multiple observer for an uncertain multiple model
77(5)
3.4 Synthesis of unknown input observers
82(11)
3.4.1 Unknown inputs affecting system state
83(4)
3.4.2 Unknown inputs affecting system state and output
87(1)
3.4.3 Estimation of unknown inputs
88(5)
3.5 Synthesis of unknown input observers: another approach
93(4)
3.5.1 Principle
93(3)
3.5.2 Multiple observers subject to unknown inputs and uncertainties
96(1)
3.6 Conclusion
97(2)
Chapter 4 Stabilization of Multiple Models
99(28)
4.1 Introduction
99(1)
4.2 Full state feedback control
99(14)
4.2.1 Linearization
101(2)
4.2.2 Specific case
103(3)
4.2.3 α-stability: decay rate
106(7)
4.3 Observer-based controller
113(6)
4.3.1 Unmeasurable decision variables
115(4)
4.4 Static output feedback control
119(7)
4.4.1 Pole placement
122(4)
4.5 Conclusion
126(1)
Chapter 5 Robust Stabilization of Multiple Models
127(32)
5.1 Introduction
127(2)
5.2 State feedback control
129(8)
5.2.1 Norm-bounded uncertainties
129(2)
5.2.2 Interval uncertainties
131(6)
5.3 Output feedback control
137(13)
5.3.1 Norm-bounded uncertainties
137(10)
5.3.2 Interval uncertainties
147(3)
5.4 Observer-based control
150(6)
5.5 Conclusion
156(1)
Conclusion
157(2)
Appendices
159(16)
Appendix 1 LMI Regions
161(6)
A1.1 Definition of an LMI region
161(1)
A1.2 Interesting LMI region examples
162(1)
A1.2.1 Open left half-plane
163(1)
A1.2.2 α-stability
163(1)
A1.2.3 Vertical band
163(1)
A1.2.4 Horizontal band
164(1)
A1.2.5 Disk of radius R, centered at (q,0)
164(1)
A1.2.6 Conical sector
165(2)
Appendix 2 Properties of M-Matrices
167(2)
Appendix 3 Stability and Comparison Systems
169(6)
A3.1 Vector norms and overvaluing systems
169(1)
A3.1.1 Definition of a vector norm
169(1)
A3.1.2 Definition of a system overvalued from a continuous process
170(2)
A3.1.3 Application
172(1)
A3.2 Vector norms and the principle of comparison
173(1)
A3.3 Application to stability analysis
174(1)
Bibliography 175(10)
Index 185
Mohammed Chadli is Associate Professor at HDR (Habilitation), University de Picardie Jules Verne, UPJV-Amiens, France.

Professor Pierre Borne, Ecole Centrale de Lille, France. He is President of the IEEE-SMC society and is presently President of the IEEE France Section.
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