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Complementarity and Variational Inequalities in Electronics - 1st Edition - ISBN: 9780128133897, 9780128133903

Complementarity and Variational Inequalities in Electronics

1st Edition

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Author: Daniel Goeleven
Paperback ISBN: 9780128133897
eBook ISBN: 9780128133903
Imprint: Academic Press
Published Date: 2nd June 2017
Page Count: 208
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Table of Contents

1. Introduction
2. On the use of complementarity problem in electronics
3. On the use of variational inequalities in electronics
4. The variational inequality model in electronics
5. A variational inequality theory
6. Non-regular dynamic systems


Complementarity and Variational Inequalities in Electronics evaluates the main mathematical models relevant to the study of electrical network problems involving devices. The book focuses on complementarity problems, variational inequalities and non-regular dynamical systems which are well-known for their applications in mechanics and economics, but rarely target electrical applications. The book uses these tools to review the qualitative properties of devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers. Users will find demonstrations on how to compute optimized output signal relevant to potentially superior applications.

In addition, the book describes how to determine the stationary points of dynamical circuits and to determine the corresponding Lyapunov stability and attractivity properties, topics of major importance for further dynamical analysis and control. Hemivariational inequalities are also covered in some depth relevant to application in thyristor devices.

Key Features

  • Reviews the main mathematical models applicable to the study of electrical networks involving diodes and transistors
  • Focuses on theoretical existence and uniqueness of a solution, stability of stationary solutions, and invariance properties
  • Provides realistic complementarity and variational problems to illustrate theoretical results
  • Evaluates applications of the theory across many devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers
  • Details both fully developed mathematical proofs and common models used in electronics
  • Provides a comprehensive literature review, including thousands of relevant references


Applied mathematicians using engineering models to illustrate their theoretical results, and mathematical engineers using mathematical tools to propose and study rigorous engineering models. Early career researchers working on complementarity problems, variational inequalities, differential inclusions and non-regular dynamical systems


No. of pages:
© Academic Press 2017
2nd June 2017
Academic Press
Paperback ISBN:
eBook ISBN:


"The mathematical results presented in the book can be useful in the study of stationary points of dynamical circuits, Lyapunov stability and attractivity problems and give interesting insight based on certain special characteristics of the nonlinear devices in the circuits." --Zentralblatt MATH 1377

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About the Author

Daniel Goeleven

Daniel Goeleven graduated in applied mathematical engineering, Facultes polytechniques, Universie Catholique de Louvain, UCL, Belgium, in 1989 and received the Ph. D degree in mathematics from the Facultes Universitaires de Namur, Belgium, in 1993. He was an FNRS researcher for two years and he held an Alexander von Humboldt postdoctoral fellowship at the RWTH Aachen, Germany in 1996. Since that time, he has been a Professor at the University of la Reunion, France. His major scientific interest concerns variation inequalities modelling and (possibly non-smooth) dynamical systems modelling with applications in different areas like unilateral mechanics, non-regular electronics, biology and biochemistry.

Affiliations and Expertise

Professor of Mathematics, University of la Reunion, France