Time-delay Systems: Analysis and Control Using the Lambert W Function

Contents......Page 9
Preface......Page 7
1.1 Motivation......Page 12
1.2.1 Delay differential equation......Page 13
1.2.2 Lambert W function......Page 14
1.3 Scope of This Document......Page 16
1.4 Original Contributions......Page 20
2.1 Introduction......Page 22
2.2.1 Generalization to free systems of DDEs......Page 24
2.2.2 Stability......Page 29
2.3 Forced Systems......Page 30
2.3.1 Generalization to systems of DDEs......Page 33
2.4 Approach Using the Laplace Transformation......Page 34
2.4.1 Scalar case......Page 35
2.4.2 Generalization to systems of DDEs......Page 36
2.5 Concluding Remarks......Page 39
3.1 Introduction......Page 42
3.2 The Chatter Equation in the Turning Process......Page 44
3.3 Solving DDEs and Stability......Page 47
3.3.1 Eigenvalues and stability......Page 48
3.4 Concluding Remarks......Page 52
4.1 Introduction......Page 54
4.2 Controllability......Page 55
4.3 Observability......Page 59
4.4 Illustrative Example......Page 61
4.5 Conclusions and Future Work......Page 65
5.1 Introduction......Page 68
5.2.2 Eigenvalue assignment......Page 70
5.3.1 Scalar case......Page 73
5.3.2 Systems with control delays......Page 75
5.3.3 Systems with state delays......Page 81
5.4 Conclusions......Page 85
6.1 Introduction......Page 86
6.2.1 Stability radius......Page 88
6.2.2 Design of robust feedback controller......Page 90
6.3 Time-Domain Specifications......Page 93
6.4 Concluding Remarks......Page 96
7.1 Introduction......Page 98
7.2 Problem Formulation......Page 100
7.2.2 Controllability, observability, and eigenvalue assignability......Page 102
7.3 Design of Observer-Based Feedback Controller......Page 103
7.3.1 Separation principle......Page 105
7.4 Application to Diesel Engine Control......Page 106
7.5 Conclusions......Page 113
8.1 Introduction......Page 116
8.2 HIV Pathogenesis Dynamic Model with an Intracellular Delay......Page 117
8.3.1 Delay effects on rightmost eigenvalues......Page 120
8.3.2 Mutation, drug efficacy and eigenvalues......Page 122
8.4.1 HIV: Eigenvalue sensitivity......Page 124
8.4.2 Eigenvalue sensitivity and response sensitivity......Page 126
8.5 Concluding Remarks and Future Work......Page 128
A.1 Commutation of Matrices A and S in Eq. (2.10)......Page 130
A.2 Reduction of Eqs. (2.31) and (2.32) to Eq. (2.36)......Page 131
B.1 Proof Regarding Minimal Energy......Page 132
B.2 Comparisons with Other Types of Controllability and Observability......Page 133
C.1 Limits in Assignment of Eigenvalues......Page 136
Bibliography......Page 140
Index......Page 152