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Introduction 1

0.1 Development of control theory 1

0.2 Structural requirements and control features of the system 5

0.3 Nonlinear control in power system 10

0.4 The main content of modern control theory 17

Chapter 1 State-space expression of control system 18

1.1 The basic concepts 18

1.2 The simulation structure diagram of state-space expression 20

1.3 The construction of state-space expression 20

1.4 The construction of state-space expression from transfer function 25

1.5 Transfer function and transfer function matrix from transfer function to state equation 30

1.6 State-space expression of composite system 31

1.7 Linear transformation 34

1.8 State-space expression of discrete system 36

Exercise 39

Chapter 2 The solution of state-space expression of control system 43

2.1 Solution of homogeneous state equation of linear time-invariant system 43

2.2 Matrix exponent 43

2.3 Homogeneous solution of time-varying system 46

2.4 State transfer matrix 61

2.5 Solution of linear continuous system non-homogeneous state equation 62

2.6 Solution of discrete-time system state equation 63

2.7 Discretization of continuous time-state-space expression 64

Exercise 65

Chapter 3 Controllability and observability of linear system 69

3.1 Controllability of time-invariant discrete system 69

3.2 Controllability of time-invariable continuous system 71

3.3 Observability of time-invariant system 75

3.4 Controllability and observability of linear time-varying system 78

3.5 The dual relation of controllability and observability 85

3.6 Structural decomposition of linear time-invariant system 86

3.7 Relation of controllability,observability and transfer function matrix 89

3.8 Controllabi lity standard and observability standard 91

3.9 System realization 93

Exercise 96

Chapter 4 Stability and Lyapunov method 100

4.1 The basic concept of stability 100

4.2 The basic idea of Lyapunov function 104

4.3 Lyapunov function stability method 108

4.4 Asymptotic stability 111

4.5 Some common construction method of Lyapunov function 118

4.6 Vector Lyapunov function 128

4.7 Application of Lyapunov methods in linear system 130

4.8 Lyapunov method in Hamilton system 133

Exercise 142

Chapter 5 Synthesis of linear time-invariant system 145

5.1 Definition and property of state feedback 145

5.2 Pole assignment 146

5.3 System stabilization problem 150

5.4 System deeoupling problem 151

5.5 State observer 158

Exercise 169

Chapter 6 Optimal control 172

6.1 Summary 172

6.2 Variational methods of solving optimal control 173

6.3 Hamilton function 178

6.4 Phorcha problem 179

6.5 Minimum principle 181

6.6 Dynamic programming 189

6.7 Linear quadratic optimal control problem 196

Exercise 198