Contents
Preface
Chapter 1 Introduction 1
1.1 Background 1
1.1.1 Nonlinear Systems Analysis 1
1.1.2 Uncertain Nonlinear Control Methods 2
1.2 Why Operator-based Robust Nonlinear Control? 3
1.3 The Content of This Book 6
References 9
Chapter 2 Mathematical Preliminaries 14
2.1 Preliminaries in Spaces and Operators 14
2.1.1 Normed Spaces 14
2.1.2 Banach Space 15
2.1.3 Extended Linear Space 15
2.1.4 Lipschitz Operators 16
2.1.5 Generalized Lipschitz Operator 17
2.1.6 Causality for Generalized Lipschitz Operator 18
2.1.7 Unimodular Operator 18
2.2 Operator-based Coprime Factorization Method 19
2.2.1 Right Coprime Factorization 19
2.2.2 Robust Right Coprime Factorization 21
References 23
Chapter 3 Extended Robust Right Coprime Factorization for Uncertain Nonlinear Systems Control 25
3.1 Introduction 25
3.2 Operator-based Extended Right Coprime Factorization 27
3.2.1 L. Operator 27
3.2.2 An Example to Explain L. Operator 29
3.2.3 Extended Right Coprime Factorization 30
3.3 Robust Control for Uncertain Nonlinear Systems Using Extended Right Coprime Factorization 32
3.3.1 Problem Statement 32
3.3.2 Su±cient Robust Condition of Robust Stability 36
3.3.3 Simulation Example 39
3.4 Conclusion and Discussion 43
References 43
Chapter 4 Nonlinear Robust Control Using Adjoint Operator-based Right Coprime Factorization 46
4.1 Introduction 46
4.2 Factorization Design Scheme of Nonlinear Systems 47
4.2.1 Problem Statement 47
4.2.2 Adjoint Operator 48
4.2.3 Factorization Method Based on Adjoint Operator 49
4.2.4 Existence of Controllers 51
4.3 Adjoint Operator-based Robust Stability Analysis 52
4.3.1 An Example for Showing Necessity of Proposed Method 52
4.3.2 Robust Su±cient Conditions 53
4.4 Simulation Example 56
4.5 Conclusion 58
References 59
Chapter 5 Robust Stability Analysis of MIMO Uncertain Nonlinear System 62
5.1 Introduction 62
5.2 Problem Statement 64
5.3 Robust Control for MIMO Uncertain Nonlinear Systems 64
5.3.1 Decoupled Design Scheme 64
5.3.2 Robust Control Based on Unimodular Operator 68
5.4 Simulation Example 69
5.5 Conclusion 75
References 75
Chapter 6 Two Steps Robust Design Scheme for Uncertain Nonlinear Systems 80
6.1 Introduction 80
6.2 Stability Analysis 82
6.2.1 Problem Statement 82
6.2.2 Two Steps Factorized Realization 82
6.3 Robust Stability Analysis Based Two Steps Factorization 86
6.3.1 Case One: Known Bounded Perturbations 87
6.3.2 Case Two: Unknown Bounded Perturbations 88
6.4 Simulation Example 89
6.5 Conclusion 92
References 93
Chapter 7 Robust Control for Uncertain Nonlinear Systems by Rejection Method 96
7.1 Introduction 96
7.2 Operator-based Framework Design 97
7.2.1 Construction Analysis of Uncertain Nonlinear Systems 97
7.2.2 Robust Stability Analysis 102
7.3 Nonlinear Systems with Unknown Disturbances Rejection 103
7.3.1 Compensator Design Scheme 103
7.3.2 Rejection Method Analysis 106
7.4 Simulation Example 110
7.5 Conclusion 116
References 116
Chapter 8 Robust Control for Nonlinear Systems with External Disturbance 120
8.1 Introduction 120
8.2 Robust Control Analysis 122
8.2.1 Problem Statement 122
8.2.2 Three Cases of Robust Conditions 123
8.2.3 Illustrative Example 127
8.3 Output Tracking Design 128
8.3.1 Problem Statement 128
8.3.2 Admissible Controllers Analysis 130
8.3.3 Internal Perturbation and External Disturbance Rejection 131
8.4 Simulation Example 134
8.5 Conclusion 138
References 138
Chapter 9 Operator-based Sensitivity Analysis and Reset Robust Control of Uncertain Nonlinear Systems 142
9.1 Introduction 142
9.2 Bilinear Operator-based Nonlinear Robust Control 143
9.2.1 Problem Statement 143
9.2.2 Bilinear Operator 144
9.2.3 Robust Stability Control 146
9.3 Sensitivity Analysis 147
9.3.1 Sensitivity of Perturbed Systems 147
9.3.2 Tracking Design Scheme 150
9.3.3 Simulation Example 153
9.4 Reset Robust Control 156
9.4.1 Reset Robust Analysis 156
9.4.2 Simulation Example 159
9.5 Conclusion 161
References 161
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