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© 2018

Theory of Hybrid Systems: Deterministic and Stochastic

  • Is the first book to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments)

  • Covers topics including switched, impulsive, and impulsive-switched systems with/without time delay and with/without random noise in one volume

  • Focuses on establishing the important system properties using the elegant Lyapunov or Lyapunov–Razumikhin methods for time-delayed systems

  • Includes results combing reliable control, H-infinity control, and ISS (input-to-state stability)

  • Presents rigorous mathematical proofs enhanced with numerous illustrative, worked-out examples and simulations

Book

Part of the Nonlinear Physical Science book series (NPS)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Mohamad S. Alwan, Xinzhi Liu
    Pages 1-4
  3. Mohamad S. Alwan, Xinzhi Liu
    Pages 5-58
  4. Mohamad S. Alwan, Xinzhi Liu
    Pages 77-95
  5. Mohamad S. Alwan, Xinzhi Liu
    Pages 97-116
  6. Mohamad S. Alwan, Xinzhi Liu
    Pages 117-134
  7. Mohamad S. Alwan, Xinzhi Liu
    Pages 135-143
  8. Mohamad S. Alwan, Xinzhi Liu
    Pages 145-163
  9. Mohamad S. Alwan, Xinzhi Liu
    Pages 165-176
  10. Mohamad S. Alwan, Xinzhi Liu
    Pages 177-190
  11. Mohamad S. Alwan, Xinzhi Liu
    Pages 191-206
  12. Mohamad S. Alwan, Xinzhi Liu
    Pages 207-227
  13. Mohamad S. Alwan, Xinzhi Liu
    Pages 229-241

About this book

Introduction

This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin–Lyapunov methods to investigate the systems’ properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.

Keywords

Hybrid Systems Time Delay Random Process Qualitative Properties Laypunov/Razumikhin Methods

Authors and affiliations

  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada

About the authors

Dr. Mohamad S. Alwan is a lecturer at the Department of Applied Mathematics at the University of Waterloo. Since 2004, his research interests have been directed towards broadening the research area of “Stochastic and Deterministic Hybrid Systems with/without Time Delay and Applications to Control Systems”. Specifically, he has been working on establishing many system properties and applying some of these properties to control systems. He has published several peer-reviewed journal papers, conference papers, and book chapters, most of which are included in the book.

Professor Xinzhi Liu is a faculty member of the Department of Applied Mathematics at the University of Waterloo. He received his Ph.D. degree in Applied Mathematics from the University of Texas at Arlington. He is an expert on hybrid dynamical systems, stability theory and control methods. He has been the editor-in- chief of the Journal--Dynamics of Continuous, Discrete and Impulsive Systems since 1995. He has published over 300 research papers and 3 monographs and 20 edited books on different topics in the field of dynamical systems.

 

Bibliographic information

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