分数阶非线性系统的稳定性分析与综合（英文版）

Contents
Preface
Chapter 1 Introduction 1
1.1 Brief historical ovder lew 1
1.1.1 Fractional order systems 1
1.1.2 Fractionru order neural networks 2
1.1.3 T-S fuzzy systems 3
1.1.4 Synchronization 3
1.1.5 Adaptive control 4
1.1 6 Sliding mode control 5
1.1.7 Tacking control 5
1.1.8 Type-2 fuZzy control 5
1.1.9 H∞， Ipassive performance 6
1.2 Why fractional order 7
1.3 Organization of the book.8
References11
Chapter 2 Fundamentals of fractiona1-order system8 21
2.1 Several important fimctions of fractional calculus 21
2.2 Fractional integral and derivatives 23
2.3 Some important lemmas 26
References 28
Chapter 3 Exponential stability analysis of fractiona1-order T-S PlZzy neural networks 30
3.1 Problem statement 30
3.2 Stability esal ySlS 34
3.3 Numerical Examples 38
3.4 Conclusions 42
References 43
Chapter 4 Adaptive projective synchronization for fractional-order T-S fuzzy neural networks.44
4.1 Problem statement 45
4.2 Synchronization controller design and analysis 47
4.2.1 Controller desJ.gn 47
4.2.2 Stability analyse 48
4.3 Numerical simulation 52
4.3.1 Numerical example 52
4.3.2 Application to secure communications 56
4.4 Conclusions 58
References 59
Chapter 5 Projective synchronization for two nonidentical timeesdelayed fractional-order T-S fuzzy neural networks 61
5.1 Problemstatement 62
5.2 Synchronization controller design and analysis 66
5.2.1 Sliding mode controller design 66
5.2.2 Stability analysis 70
5.3 Numerical simu1ation 75
5.4 Conclusions 79
R.eferences 80
Chapter 6 Adaptive projestive synchronization for time-delayed
fractional-order neural networks 82
6.1 Problemstatement 82
6.2 Synchronization controller design and analysis 84
6.2.1 Controller design 84
6.2.2 Stability analysis 85
6.3 Numerical simulation 89
6.3.1 Numerical simulation 89
6.3.2 Application to escure ∞>InInUmestions 92
6.3.3 Comparmn exesnple 96
6.4 Conclusions 97
R.eferences 97
Chapter 7 Mixed H∞， /passive projective synchronization for fractional-order neural networks99
7.1 Problemstatement 99
7.2 Synchronization controller design and analysis 102
7.2.1 Adaptive controller design 102
7.2.2 Perlormance analysis 104
7.3 Nnmerical simulation 109
7.3.1 Numerical simulation: Case 1 109
7.3.2 Application to secure communiex止ions 112
7.3.3 Numericalsimulation: Case 2 114
7.4 Conclusions 115
References 116
Chapter 8 Mixed H∞， /passive projective synchronization for nonidentical uncertain fractional-order neural networks 117
8.1 Problem statement117
8.2 Sliding mode controller design and analysis 120
8.2.1 Sliding mode controller design 120
8.2.2 Stability analysis 122
8.3 Numerical Simulation 128
8.4 Conclusions 133
References 133
Chapter 9 Mixed H∞， md passive projective synchronization for fractional-order memristor-based neural networks 135
9.1 Problemstatement 136
9.2 Synchronization controller design and analysis 141
9.2.1 Controller design 141
9.2.2 Stability analysis 142
9.3 Numerical simulation148
9.3.1 Three-dimension memristor-based fractional-order neural networks 148
9.3.2 Thr dimension fractional-order Hopfield neural networks 153
9.4 Conclusions 155
References 155
Chapter 10 Adaptive sliding mode projective synchronization for fractional-order memristor-based neural networks 157
10.1 problemstatement 157
10.2 Main Results 162
10.3 Num，erical simulation 170
10.3.1 Three dimeeslon memristor-based fractional-order neural networkswith time-varying delays 170
10.3.2 Thr.，.←dimeeslon fractional-ordesHopfield neural networks withfixed thne delays 176
10.4 Conclusions 178
References 178
Chapter 11 H∞， tracking control for nonlinear fractional-order systems via output feedback design 179
11.1 Problem Statement 179
11.2 Main results 181
11.2.1 Stability analysis 182
11.2.2 Controller design 184
11.3 Numerical Example 187
11.4 Conclsesese 189
Chapter 12 Adaptive interval typ-2 fuzzy sliding mode control for fractional-order nonlinear systems 190
12.1 Interval typE？ 2 fuzzy logic system 190
12.2 Main result 193
12.2.1 Controller design 193
12.2.2 Finite time stability analysis 198
12.3 Num.erical example 200
12.3.1 Application to fractional-order Lorenz chestic system 200
12.3.2 Application to a chestic non-autonomoeselectromechmical transducer model 204
12.3.3 Comparison example 206
12.4 Concles10ns 207
References 207