Nonsmooth modeling and simulation for switched circuits.
type: Item
instance of: scholarly article
title: Nonsmooth modeling and simulation for switched circuits.
zbMATH Open document ID: 1208.94003
DOI: 10.1007/978-90-481-9681-4
author: Vincent Acary
author: O. Bonnefon
author: B. Brogliato
published in: Lecture Notes in Electrical Engineering
publication date: 2010-08-03T00:00:00Z
review text: The book under review is divided into three parts. In the first part the theoretical background behind the circuits is presented. In this part there are two chapters. The first one is an introduction to switched circuits, such as RCD, RCD, RLZD, RCZD, order-two and order-three circuits. The second chapter is devoted to present the mathematical tools which are used in the book to analyze the nonsmooth circuits and their time-discretizations. The results are given without proofs. A brief recall of some basic tools and to the circuits of chapter 1 is done and their dynamics using new mathematical frameworks are rewritten. Many of the tools which are presented in this chapter, will be used, or presented in another way in chapter 4. In the third chapter, some basic facts on the circuit equation formulation and simulation which are shared by most of the analog SPICE-like simulators are presented. The formulation of the circuit equations is based on two basic ingredients: conservative laws given by the Kirchhoff laws in currents and voltages and constitutive equations of the electrical components, which lead to a Differential Algebraic Equation (DAE). The fourth chapter is an approach to NonSmooth Dynamical Systems (NSDS). Standard description of elements by means of explicit and smooth functions is enriched by new elements described by generalized equations. The characteristics of the electronic devices can be then nonsmooth and even multivalued. These elements are called the electrical ``nonsmooth elements''. The description of nonsmooth components relies a lot on mathematical notions from Convex Analysis and Mathematical Programming theory. In this chapter, the authors take advantage of the material of the foregoing chapters to arrive at the general mathematical formalisms which are used in the NSDS approach to simulate the electrical circuits of chapters 7 and 8. In chapter 5, several mathematical formalisms are presented. These formalisms incorporate not only the nons…
reviewed by: Eleonor Ciurea
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 94Cxx
zbMATH DE Number: 5763647
zbMATH Keywords: order-two circuits
zbMATH Keywords: order-three circuits
zbMATH Keywords: nonsmooth circuits
zbMATH Keywords: analog simulators
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-90-481-9681-4
OpenAlex ID: W4214764776
description: scientific article; zbMATH DE number 5763647