Contents
Introduction 1
1.1 A Brief History 1
1.2 Examples in Science and Engineering 3
1.3 Classifications of Impulsive Systems 23
1.4 A Relation with Intermittent Control 28
1.5 Overview of This Book 31
2 Definitions and Basic Theory 33
2.1 Existence and Uniqueness of Solutions 33
2.2 Controllability and Observability 37
2.2.1 Controllability 40
2.2.2 Observability 48
2.3 Fundamental Concepts 55
2.3.1 Relevant Definitions 55
2.3.2 Relevant Lemmas 60
2.3.3 Linear Matrix Inequality 61
2.3.4 Schur's Complement 63
2.3.5 Comparison Principle 64
3 Impulsive Delayed Systems 67
3.1 Lyapunov Stability 67
3.1.1 Lyapunov-Razumikhin Approach 68
3.1.2 Lyapunov-Krasovski Approach 112
3.1.3 Halanay Inequality Technique 121
3.1.4 Comparison Principle 147
3.2 Finite-Time Stability 169
3.2.1 FTS-I 171
3.2.2 FTS-II 182
3.2.3 Numerical Examples 200
3.3 Input-to-State Stability 213
3.3.1 Stabilizing or Destabilizing Impulses 215
3.3.2 Hybrid Impulses 217
3.3.3 Numerical Examples 228
3.4 Summary 231
4 Impulsive Systems with Delayed Impulses 233
4.1 Lyapunov Stability 233
4.1.1 Time-Dependent Delayed Impulses 234
4.1.2 State-Dependent Delayed Impulses 255
4.1.3 Additional Results on State-Dependent Delay 274
4.1.4 Numerical Examples 285
4.2 Input-to-State Stability
4.2.1 Stabilizing or Destabilizing Delayed Impulses 297
4.2.2 Hybrid Delayed Impulses 315
4.2.3 Numerical Examples 321
4.3 Synchronization via Delayed Impulsive Control 324
4.3.1 Impulses with Stabilizing Delays 324
4.3.2 Impulses with Destabilizing Delays 332
4.3.3 Numerical Examples 340
4.4 Summary 347
5 Impulsive Systems with Event-Triggered Mechanism 349
5.1 Lyapunov Stability 349
5.1.1 ETM of Impulsive Systems without Delays
5.1.2 ETM of Impulsive Systems with Delays 358
5.1.3 Event-Triggered Delayed Impulsive Control 365
5.1.4 Numerical Examples 373
5.2 Input-to- State Stability 382
5.2.1 State-Based Event-Triggered Impulsive Control 383
5.2.2 Output-Based Event-Triggered Impulsive Control 394
5.2.3 Numerical Examples 404
5.3 Summary 413
Bibliography 415
Index 431