现代控制理论

PrefAce
ChApter 0 BAckgrounds 1
0.1 Development of Control Theory 1
0.2 MAin Contents of Modern Control Theory 2
ChApter 1 MAthemAticAl Description of Systems . 4
1.1 ExAmple 4
1.2 BAsic Definitions 5
1.3 System Descriptions 6
1.4 Finding StAte EquAtions from High-DifferentiAl OperAtor RepresentAtion . 7
1.4.1 ControllAble CAnonicAl Form 7
1.4.2 ObservAble CAnonicAl Form . 9
1.4.3 Other SpeciAl Form 9
1.5 Block DiAgrAm . 11
1.6 TrAnsfer Function from StAte SpAce RepresentAtion . 12
1.6.1 Definition . 12
1.6.2 CAlculAtion for the TrAnsfer Function MAtrix . 13
1.7 Composite Systems 14
1.7.1 TAndem Connection 15
1.7.2 PArAllel Connection . 16
1.7.3 FeedbAck Connection 17
1.8 EquivAlent TrAnsformAtion . 17
1.8.1 EquivAlent TrAnsformAtion of the StAte SpAce Description for LineAr
Systems 17
1.8.2 DiAgonAl CAnonicAl Form And JordAn CAnonicAl Form of the System . 18
1.8.3 InvAriAnce of the System MAtrix And TrAnsfer Function MAtrix 20
1.9 ApplicAtion of MATLAB in the RepresentAtion of LineAr Systems . 21
1.10 Exercises 25
ChApter 2 Solutions 27
2.1 StAte TrAnsition MAtrix . 27
2.2 MAtrix ExponentiAl 30

2.5.1 DiscretizAtion of LineAr Discrete Time-InvAriAnt Systems 41
2.5.2 Solutions of the LineAr Discrete Time-InvAriAnt Systems 43
2.6 MATLAB for LineAr System Motion AnAlysis 43
2.7 Exercises . 47
ChApter 3 ControllAbility And ObservAbility 49
3.1 Definitions 49
3.1.1 ControllAbility 50
3.1.2 ObservAbility . 50
3.2 Con trollAbility of LineAr Continuous Systems . 51
3.2.1 Time-InvAriAnt Systems 51
3.2.2 Time-VArying Systems . 57
3.2.3 ControllAbility Index 57
3.3 ObservAbility of LineAr Continuous Systems 58
3.3.1 Time-InvAriAnt Systems 58
3.3.2 Time-VArying Systems . 60
3.3.3 ObservAbility Index . 60
3.4 Principle of DuAlity 61
3.5 ControllAble And ObservAble CAnonicAl Forms of SISO 62
3.6 StructurAl Decomposition of LineAr Systems 65
3.6.1 ControllAbility And ObservAbility of LineAr Time-InvAriAnt Systems with
NonsingulAr TrAnsformAtion 65
3.6.2 ControllAbility Decomposition 65
3.6.3 ObservAble Decomposition . 68
3.6.4 CAnonicAl Decomposition 68
3.7 MATLAB ApplicAtion for ControllAbility And ObservAbility . 69
3.8 Exercises . 73
ChApter 4 Irreducible ReAlizAtions . 75
4.1 Introduction 75
4.2 The ReAlizAtion of TrAnsfer Function MAtrix of SISO Control Systems 75
4.3 The ReAlizAtion of TrAnsfer Function MAtrix of MIMO Control Systems . 77
4.4 The MinimAl ReAlizAtion 80
4.5 Irreducible ReAlizAtion by MATLAB 83
4.6 Exercises . 86

5.2.4 The Second Method of LyApunov 102
5.2.5 KrAsovsky DiscriminAnce . 106
5.2.6 VAriAble GrAdient Method 108
5.3 ApplicAtion of MATLAB in StAbility 110
5.4 Exercises 112
ChApter 6 FeedbAcks . 114
6.1 Definitions . 114
6.1.1 StAte FeedbAcks 114
6.1.2 Output FeedbAcks . 115
6.1.3 DerivAtive FeedbAck 115
6.2 The Effects of ControllAbility And ObservAbility by FeedbAck 115
6.2.1 StAte FeedbAcks 115
6.2.2 Output FeedbAcks . 116
6.3 Pole Assignment . 117
6.3.1 SISO CAse 118
6.3.2 MIMO CAse 121
6.4 StAbilizAtion 123
6.5 Decoupling 124
6.5.1 The StAtement of Decoupling Control Problem 124
6.5.2 NecessAry And Sufficient Conditions for Decoupling Systems with
the StAte FeedbAck 125
6.6 ApplicAtion of MATLAB in FeedbAck . 128
6.6.1 StAte FeedbAck And Pole Assignment by MATLAB . 128
6.6.2 Decoupling by MATLAB . 132
6.7 Exercises 137
ChApter 7 Observers . 140
7.1 BAsic Concepts 140
7.2 Full-DimensionAl StAte Observers 141
7.3 Reduced-DimensionAl StAte Observers . 143
7.4 FeedbAck System with StAte Observers 146
7.5 Design StAte Observers by MATLAB 148
7.6 Exercises 150
ChApter 8 OptimAl Control 152
8.1 OptimAl Control Problems 152

8.2.4 The CAlculus of VAriAtion 159
8.3 LineAr QuAdrAtic RegulAtor Problems . 161
8.3.1 The StAtement of LQR 161
8.3.2 The Finite-Time StAte RegulAtor Problems 162
8.3.3 The Infinite-Time StAte-RegulAtor Problems . 165
8.3.4 The Output-RegulAtor Problems 166
8.3.5 The TrAcking Problems 167
8.4 The ApplicAtion of MATLAB in OptimAl Control Problems 169
8.5 Exercises 174
BibliogrAphy 176