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Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Kazuo Tanaka, Hua O. Wang
Copyright 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-32324-1
�½
Hardback
.
; 0-471-22459-6
�½
Electronic
.
FUZZY CONTROL SYSTEMS
DESIGN AND ANALYSIS
FUZZY CONTROL SYSTEMS
DESIGN AND ANALYSIS
A Linear Matrix Inequality Approach
KAZUO TANAKA and HUA O. WANG
A Wiley-Interscience Publication
JOHN WILEY & SONS, INC.
New York
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Chichester
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Weinheim
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Brisbane
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Singapore
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Toronto
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2001 by John Wiley & Sons, Inc. All rights reserved.
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ISBN 0-471-22459-6
This title is also available in print as ISBN 0-471-32324-1
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CONTENTS
PREFACE
ACRONYMS
1
INTRODUCTION
1.1
1.2
2
A Control Engineering Approach to Fuzzy Control
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1
Outline of This Book
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2
xi
xiii
1
TAKAGI-SUGENO FUZZY MODEL AND PARALLEL
DISTRIBUTED COMPENSATION
2.1
2.2
Takagi-Sugeno Fuzzy Model
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6
Construction of Fuzzy Model
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9
2.2.1 Sector Nonlinearity
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10
2.2.2 Local Approximation in Fuzzy Partition
Spaces
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23
Parallel Distributed Compensation
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25
A Motivating Example
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26
Origin of the LMI-Based Design Approach
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29
2.5.1 Stable Controller Design via Iterative
Procedure
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30
2.5.2 Stable Controller Design via Linear Matrix
Inequalities
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34
5
2.3
2.4
2.5
v
vi
CONTENTS
Application: Inverted Pendulum on a Cart
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38
2.6.1 Two-Rule Modeling and Control
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38
2.6.2 Four-Rule Modeling and Control
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42
Bibliography
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47
3
LMI CONTROL PERFORMANCE CONDITIONS
AND DESIGNS
Stability Conditions
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49
Relaxed Stability Conditions
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52
Stable Controller Design
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58
Decay Rate
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62
Constraints on Control Input and Output
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66
3.5.1 Constraint on the Control Input
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66
3.5.2 Constraint on the Output
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68
3.6 Initial State Independent Condition
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68
3.7 Disturbance Rejection
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69
3.8 Design Example: A Simple Mechanical System
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76
3.8.1 Design Case 1: Decay Rate
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78
3.8.2 Design Case 2: Decay Rate
q
Constraint on the
Control Input
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79
3.8.3 Design Case 3: Stability
q
Constraint on the Control
Input
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80
3.8.4 Design Case 4: Stability
q
Constraint on the Control
Input
q
Constraint on the Output
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81
References
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81
4
FUZZY OBSERVER DESIGN
Fuzzy Observer
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83
Design of Augmented Systems
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84
4.2.1 Case A
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85
4.2.2 Case B
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90
4.3 Design Example
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93
References
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96
5
ROBUST FUZZY CONTROL
5.1 Fuzzy Model with Uncertainty
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98
5.2 Robust Stability Condition
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98
5.3 Robust Stabilization
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105
References
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108
97
4.1
4.2
83
3.1
3.2
3.3
3.4
3.5
2.6
49

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