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Chapter 1 System Model 1

1.1 Introduction 1

1.2 Models of Systems 1

1.2.1 Differential Equation 1

1.2.2 Transfer Function 4

1.2.3 The State-space Model 7

1.3 Transition from One Mathematical Model to Another 17

1.3.1 From Differential Equation to Transfer Function for SISO Systems 17

1.3.2 From Transfer Function to Differential Equation for SISO Systems 18

1.3.3 From G(s)to g(t) and Vice Versa 18

1.3.4 From State Equations to Transfer Function Matrix 18

1.3.5 From Transfer Function Matrix to State Equations for SISO Systems 20

1.4 Summary 23

Appendix:Three Power Generation Models 23

Exercise 29

Chapter 2 Linear Transformation of State Vector 32

2.1 Linear Algebra 32

2.2 Transform to Diagonal Form and Jordan Form 37

Exercise 46

Chapter 3 Solution of State Space Model 48

3.1 Introduction 48

3.2 Solution of LTI State Equations 48

3.3 State Transfer Matrix 51

3.3.1 Properties 51

3.3.2 Calculating the state transition matrix 55

3.4 Discretization 63

3.5 Solution of Discrete-Time Equation 65

3.6 Summary 72

Exercise 72

Chapter 4 Stable Analysis 74

4.1 Introduction 74

4.2 Definition 74

4.3 Stability Criteria 85

4.3.1 Lyapunov's Second Method 85

4.3.2 State Dynamics Stability Criteria for Continuous Linear Systems 93

4.3.3 State Dynamics Stability Criteria for Discrete Systems 101

4.4 Summary 104

Exercise 104

Chapter 5 Controllability and Observability 106

5.1 Introduction 106

5.2 Definition 107

5.2.1 Controllability 107

5.2.2 Observability 108

5.3 Criteria 109

5.3.1 Controllable Criteria 109

5.3.2 Controllable Examples 115

5.3.3 Observable Criteria 118

5.3.4 Observable Examples 120

5.4 Duality System 123

5.4.1 Definition 123

5.4.2 Properties of Duality Systems 124

5.5 Canonical Form 126

5.5.1 Controllability Canonical Form of Single-Input Systems 126

5.5.2 Observability Canonical Form of Single-Output Systems 131

5.5.3 Example 133

5.5.4 Observability and Controllability Canonical Form of Multi-Input Multi-Output Systems 136

5.6 System Decomposition 137

5.6.1 Controllability Decomposition 137

5.6.2 Observability Decomposition 140

5.6.3 Controllability and Observability Decomposition 143

5.6.4 Minimum Realization 148

5.7 Summary 155

Exercise 156

Chapter 6 State Feedback and Observer 159

6.1 Introduction 159

6.2 Linear Feedback 159

6.2.1 State Feedback 159

6.2.2 Output Feedback 160

6.2.3 Feedback from output to ？ 161

6.3 Pole Assignment 162

6.3.1 Sufficient and Necessary Condition for Arbitrary Pole Assignment 162

6.3.2 Methods to Assign the Poles of a System 165

6.3.3 Examples 169

6.4 State Estimator 174

6.4.1 Introduction 174

6.4.2 State Estimator 174

6.5 State Feedback Based on State Estimator 187

6.6 Summary 189

Appendix:State Feedback and Observer for Main Steam-temperature Control in Power Plant Steam-boiler Generation System 190

Exercises 193

参考文献 196