非线性物理科学 混合系统理论 确定系统和随机系统PDF电子书下载

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1 Motivating Examples 1

1.1 Switched Systems 1

1.1.1 Supervisory Switching Control 1

1.1.2 Switched Server System 2

1.1.3 Singular System with Markov Switching 2

1.2 Impulsive Systems 3

1.2.1 SEIRS Epidemic Model with Impulse Vaccinations 3

1.2.2 Insulin Treatment 4

References 4

2 Mathematical Background 5

2.1 Basic Definitions 5

2.2 Comparison Method 10

2.3 Delay Systems 12

2.4 Impulsive Systems 15

2.5 Comparison Method for Impulsive Systems 20

2.6 Impulsive Systems with Time Delay 22

2.7 Stochastic Differential Equations 24

2.7.1 Notations and Basic Definitions 24

2.7.2 Stochastic Processes 27

2.7.3 Stochastic Differential Equations 29

2.7.4 Comparison Method for Stochastic Systems 35

2.8 Stochastic Impulsive System with Time Delay 36

2.9 Switched Systems 38

2.9.1 System Formulation 38

2.9.2 Systems with Stable Subsystems 41

2.10 Stochastic Switched Systems with Time Delay 44

2.11 Singularly Perturbed Systems 49

2.12 Miscellaneous Results 52

2.13 Notes and Comments 54

References 55

3 Fundamental Properties of Stochastic Impulsive Systems with Time Delay 59

3.1 Existence of Solution 61

3.2 Forward Continuation 69

3.3 Global Existence 72

3.4 Uniqueness of Solution 73

3.5 Notes and Comments 74

References 75

4 Stability of Stochastic Impulsive Systems with Time Delay 77

4.1 Stability Analysis by Classical Lyapunov Technique 78

4.2 Stability Analysis by Comparison Method 85

4.3 Notes and Comments 95

References 95

5 Large-Scale Stochastic Impulsive Systems with Time Delay 97

5.1 Problem Formulation 97

5.2 Analysis by Lyapunov Method 101

5.3 Comparison Method 105

5.3.1 Method of Lyapunov Function 105

5.3.2 Method of Vector Lyapunov Functions 107

5.4 Examples 111

5.5 Notes and Comments 116

References 116

6 Input-to-State Stability for Stochastic Switched Systems 117

6.1 Problem Formulation 117

6.2 Initial-State-Dependent Dwell-Time 121

6.3 Markovian Switching 128

6.4 Notes and Comments 133

References 134

7 Reliable Control for Stochastic Switched Systems with State Delay 135

7.1 Problem Formulation 135

7.2 Stability Analysis 137

7.3 Numerical Example 140

7.4 Notes and Comments 142

References 142

8 Robust Reliable Control for Impulsive Large-Scale Systems 145

8.1 Problem Formulation 145

8.2 Reliable Control 147

8.3 State Estimation 156

8.4 Notes and Comments 163

References 163

9 Switched Singularly Perturbed Systems with Time Delay 165

9.1 Problem Formulation 165

9.2 Stability Analysis 166

9.2.1 Linear Systems 166

9.2.2 Nonlinear Systems 171

9.3 Notes and Comments 175

References 175

10 Singularly Perturbed Impulsive-Switched Systems with Time Delay 177

10.1 Problem Formulation 177

10.2 Stability Analysis 178

10.2.1 Linear Systems 178

10.2.2 Nonlinear Systems 186

10.3 Notes and Comments 190

Reference 190

11 Stabilization and State Estimation via Sliding Mode Control 191

11.1 Problem Formulation 191

11.2 Slow Sliding Mode Control Design 192

11.2.1 Sliding Mode Control with Multiple Inputs 193

11.2.2 Reachability Analysis 194

11.3 Sliding Mode Luenberger Observer 198

11.4 Numerical Examples 202

11.5 Notes and Comments 205

References 206

12 Comparison Method and Stability of EPCA 207

12.1 Introduction 207

12.2 Problem Formulation 208

12.3 Comparison Method 210

12.4 Stability Analysis 216

12.5 Numerical Examples 222

12.6 Application 225

12.7 Notes and Comments 226

References 227

13 Existence,Uniqueness and Stability of Stochastic EPCA 229

13.1 Existence and Uniqueness of Solutions 230

13.2 Comparison Method 236

13.3 Stability Analysis 238

13.4 Notes and Comments 241

References 241

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