Complementarity and Variational Inequalities in Electronics

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 transistorsFocuses on theoretical existence and uniqueness of a solution, stability of stationary solutions, and invariance propertiesProvides realistic complementarity and variational problems to illustrate theoretical resultsEvaluates applications of the theory across many devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiersDetails both fully developed mathematical proofs and common models used in electronicsProvides a comprehensive literature review, including thousands of relevant references

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