Goeleven D. Complementarity and Variational Inequalities in Electronics

Academic Press, 2017. — 202 p. — (Mathematical Analysis and its Applications). — ISBN: 978-0-12-813389-7.This book 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 FeaturesReviews 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 referencesApplied 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 systemsOn the use of complementarity problem in electronics
On the use of variational inequalities in electronics
The variational inequality model in electronics
A variational inequality theory
Non-regular dynamic systems