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Table of contents

  1. Front Matter
    Pages i-ix
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Xinzhi Liu, Kexue Zhang
      Pages 3-7
  3. Discrete-Time Impulsive Systems

    1. Front Matter
      Pages 9-9
    2. Xinzhi Liu, Kexue Zhang
      Pages 61-70
  4. Continuous-Time Impulsive Systems

    1. Front Matter
      Pages 71-71
    2. Xinzhi Liu, Kexue Zhang
      Pages 73-96
    3. Xinzhi Liu, Kexue Zhang
      Pages 97-139
    4. Xinzhi Liu, Kexue Zhang
      Pages 141-177
  5. Impulsive Systems on Time Scales

    1. Front Matter
      Pages 179-179
    2. Xinzhi Liu, Kexue Zhang
      Pages 181-212
    3. Xinzhi Liu, Kexue Zhang
      Pages 285-301
  6. Conclusions and Future Work

    1. Front Matter
      Pages 303-303
    2. Xinzhi Liu, Kexue Zhang
      Pages 305-308
  7. Back Matter
    Pages 309-321

About this book

Introduction

This monograph discusses the issues of stability and the control of impulsive systems on hybrid time domains, with systems presented on discrete-time domains, continuous-time domains, and hybrid-time domains (time scales). Research on impulsive systems has recently attracted increased interest around the globe, and significant progress has been made in the theory and application of these systems. This book introduces recent developments in impulsive systems and fundamentals of various types of differential and difference equations. It also covers studies in stability related to time delays and other various control applications on the different impulsive systems. In addition to the analyses presented on dynamical systems that are with or without delays or impulses, this book concludes with possible future directions pertaining to this research.

Keywords

impulsive systems time scales time-delay stability synchornization Lyapunov function Krasocskii-Lyapunov functional Razumikhin technique

Authors and affiliations

  • Xinzhi Liu
    • 1
  • Kexue Zhang
    • 2
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-06212-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-06211-8
  • Online ISBN 978-3-030-06212-5
  • Series Print ISSN 1574-0463
  • Buy this book on publisher's site
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