Complementarity and Variational Inequalities in Electronics

ISBN-13: 9780128133897 / Angielski / Miękka / 2017 / 208 str.

Daniel Goeleven

Opis

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.

• 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

Recenzje

"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

Spis treści

1. Introduction2. On the use of complementarity problem in electronics3. On the use of variational inequalities in electronics4. The variational inequality model in electronics5. A variational inequality theory6. Non-regular dynamic systems

O autorze

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.