Impulsive Systems with Delays: Stability and Control

✍ Scribed by Xiaodi Li, Shiji Song

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 449
• Edition: 1
• Category: Library

✦ Synopsis

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.

This book will be of use to specialists who are interested in the theory of impulsive differential equations and impulsive control theory, as well as high technology specialists who work in the fields of complex networks and applied mathematics. Also, instructors teaching graduate courses and graduate students will find this book a valuable source of nonlinear system theory.

✦ Table of Contents

Preface
Acknowledgements
Contents
Notations
Sets and Spaces
Norms
Set Theory
Vector and Matrix Operators
Mathematical Symbols
Abbreviations
Miscellaneous
1 Introduction
1.1 A Brief History
1.2 Examples in Science and Engineering
1.3 Classifications of Impulsive Systems
1.4 A Relation with Intermittent Control
1.5 Overview of This Book
2 Definitions and Basic Theory
2.1 Existence and Uniqueness of Solutions
2.2 Controllability and Observability
2.2.1 Controllability
2.2.2 Observability
2.3 Fundamental Concepts
2.3.1 Relevant Definitions
2.3.2 Relevant Lemmas
2.3.3 Linear Matrix Inequality
2.3.4 Schur's Complement
2.3.5 Comparison Principle
3 Impulsive Delayed Systems
3.1 Lyapunov Stability
3.1.1 Lyapunov-Razumikhin Approach
3.1.2 Lyapunov-Krasovskii Approach
3.1.3 Halanay Inequality Technique
3.1.4 Comparison Principle
3.2 Finite-Time Stability
3.2.1 FTS-I
3.2.2 FTS-II
3.2.3 Numerical Examples
3.3 Input-to-State Stability
3.3.1 Stabilizing or Destabilizing Impulses
3.3.2 Hybrid Impulses
3.3.3 Numerical Examples
3.4 Summary
4 Impulsive Systems with Delayed Impulses
4.1 Lyapunov Stability
4.1.1 Time-Dependent Delayed Impulses
4.1.2 State-Dependent Delayed Impulses
4.1.3 Additional Results on State-Dependent Delay
4.1.4 Numerical Examples
4.2 Input-to-State Stability
4.2.1 Stabilizing or Destabilizing Delayed Impulses
4.2.2 Hybrid Delayed Impulses
4.2.3 Numerical Examples
4.3 Synchronization via Delayed Impulsive Control
4.3.1 Impulses with Stabilizing Delays
4.3.2 Impulses with Destabilizing Delays
4.3.3 Numerical Examples
4.4 Summary
5 Impulsive Systems with Event-Triggered Mechanism
5.1 Lyapunov Stability
5.1.1 ETM of Impulsive Systems without Delays
5.1.2 ETM of Impulsive Systems with Delays
5.1.3 Event-Triggered Delayed Impulsive Control
5.1.4 Numerical Examples
5.2 Input-to-State Stability
5.2.1 State-Based Event-Triggered Impulsive Control
5.2.2 Output-Based Event-Triggered Impulsive Control
5.2.3 Numerical Examples
5.3 Summary
Appendix Bibliography
Index