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This book systematically presents the most recent progress in stability and control of impulsive systems with delays. Impulsive systems have recently attracted continued high research interests because they provide a natural framework for mathematical modeling of many real-world processes. It focuses not only on impulsive delayed systems， but also impulsive systems with delayed impulses and impulsive systems with event-triggered mechanism， including their Lyapunov stability， finite-time stability and input-to-state stability synthesis. Special attention is paid to the bilateral effects of the delayed impulses， where comprehensive stability properties are discussed in the framework of time-dependent and state-dependent delays. New original work with event-triggered impulsive control and its applications in multi-agent systems and collective dynamics are also provided.
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ContentsIntroduction 11.1 A Brief History 11.2 Examples in Science and Engineering 31.3 Classifications of Impulsive Systems 231.4 A Relation with Intermittent Control 281.5 Overview of This Book 312 Definitions and Basic Theory 332.1 Existence and Uniqueness of Solutions 332.2 Controllability and Observability 372.2.1 Controllability 402.2.2 Observability 482.3 Fundamental Concepts 552.3.1 Relevant Definitions 552.3.2 Relevant Lemmas 602.3.3 Linear Matrix Inequality 612.3.4 Schurs Complement 632.3.5 Comparison Principle 643 Impulsive Delayed Systems 673.1 Lyapunov Stability 673.1.1 Lyapunov-Razumikhin Approach 683.1.2 Lyapunov-Krasovski Approach 1123.1.3 Halanay Inequality Technique 1213.1.4 Comparison Principle 1473.2 Finite-Time Stability 1693.2.1 FTS-I 1713.2.2 FTS-II 1823.2.3 Numerical Examples 2003.3 Input-to-State Stability 2133.3.1 Stabilizing or Destabilizing Impulses 2153.3.2 Hybrid Impulses 2173.3.3 Numerical Examples 2283.4 Summary 2314 Impulsive Systems with Delayed Impulses 2334.1 Lyapunov Stability 2334.1.1 Time-Dependent Delayed Impulses 2344.1.2 State-Dependent Delayed Impulses 2554.1.3 Additional Results on State-Dependent Delay 2744.1.4 Numerical Examples 2854.2 Input-to-State Stability4.2.1 Stabilizing or Destabilizing Delayed Impulses 2974.2.2 Hybrid Delayed Impulses 3154.2.3 Numerical Examples 3214.3 Synchronization via Delayed Impulsive Control 3244.3.1 Impulses with Stabilizing Delays 3244.3.2 Impulses with Destabilizing Delays 3324.3.3 Numerical Examples 3404.4 Summary 3475 Impulsive Systems with Event-Triggered Mechanism 3495.1 Lyapunov Stability 3495.1.1 ETM of Impulsive Systems without Delays5.1.2 ETM of Impulsive Systems with Delays 3585.1.3 Event-Triggered Delayed Impulsive Control 3655.1.4 Numerical Examples 3735.2 Input-to- State Stability 3825.2.1 State-Based Event-Triggered Impulsive Control 3835.2.2 Output-Based Event-Triggered Impulsive Control 3945.2.3 Numerical Examples 4045.3 Summary 413Bibliography 415Index 431
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