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Nonsmooth Modeling and Simulation for Switched Circuits concerns
the modeling and the numerical simulation of switched circuits with
the nonsmooth dynamical systems (NSDS) approach, using
piecewise-linear and multivalued models of electronic devices like
diodes, transistors, switches. Numerous examples (ranging from
introductory academic circuits to various types of power
converters) are analyzed and many simulation results obtained with
the INRIA open-source SICONOS software package are presented.
Comparisons with SPICE and hybrid methods demonstrate the power of
the NSDS approach. Nonsmooth Modeling and Simulation for Switched
Circuits is intended to researchers and engineers in the field of
circuits simulation and design, but may also attract applied
mathematicians interested by the numerical analysis for nonsmooth
dynamical systems, as well as researchers from Systems and Control.
This book concerns the numerical simulation of dynamical systems
whose trajec- ries may not be differentiable everywhere. They are
named nonsmooth dynamical systems. They make an important class of
systems, rst because of the many app- cations in which nonsmooth
models are useful, secondly because they give rise to new problems
in various elds of science. Usually nonsmooth dynamical systems are
represented as differential inclusions, complementarity systems,
evolution va- ational inequalities, each of these classes itself
being split into several subclasses. The book is divided into four
parts, the rst three parts being sketched in Fig. 0. 1. The aim of
the rst part is to present the main tools from mechanics and
applied mathematics which are necessary to understand how nonsmooth
dynamical systems may be numerically simulated in a reliable way.
Many examples illustrate the th- retical results, and an emphasis
is put on mechanical systems, as well as on electrical circuits
(the so-called Filippov's systems are also examined in some detail,
due to their importance in control applications). The second and
third parts are dedicated to a detailed presentation of the
numerical schemes. A fourth part is devoted to the presentation of
the software platform Siconos. This book is not a textbook on -
merical analysis of nonsmooth systems, in the sense that despite
the main results of numerical analysis (convergence, order of
consistency, etc. ) being presented, their proofs are not provided.
Nonsmooth Modeling and Simulation for Switched Circuits concerns
the modeling and the numerical simulation of switched circuits with
the nonsmooth dynamical systems (NSDS) approach, using
piecewise-linear and multivalued models of electronic devices like
diodes, transistors, switches. Numerous examples (ranging from
introductory academic circuits to various types of power
converters) are analyzed and many simulation results obtained with
the INRIA open-source SICONOS software package are presented.
Comparisons with SPICE and hybrid methods demonstrate the power of
the NSDS approach. Nonsmooth Modeling and Simulation for Switched
Circuits is intended to researchers and engineers in the field of
circuits simulation and design, but may also attract applied
mathematicians interested by the numerical analysis for nonsmooth
dynamical systems, as well as researchers from Systems and Control.
This book concerns the numerical simulation of dynamical systems
whose trajec- ries may not be differentiable everywhere. They are
named nonsmooth dynamical systems. They make an important class of
systems, rst because of the many app- cations in which nonsmooth
models are useful, secondly because they give rise to new problems
in various elds of science. Usually nonsmooth dynamical systems are
represented as differential inclusions, complementarity systems,
evolution va- ational inequalities, each of these classes itself
being split into several subclasses. The book is divided into four
parts, the rst three parts being sketched in Fig. 0. 1. The aim of
the rst part is to present the main tools from mechanics and
applied mathematics which are necessary to understand how nonsmooth
dynamical systems may be numerically simulated in a reliable way.
Many examples illustrate the th- retical results, and an emphasis
is put on mechanical systems, as well as on electrical circuits
(the so-called Filippov's systems are also examined in some detail,
due to their importance in control applications). The second and
third parts are dedicated to a detailed presentation of the
numerical schemes. A fourth part is devoted to the presentation of
the software platform Siconos. This book is not a textbook on -
merical analysis of nonsmooth systems, in the sense that despite
the main results of numerical analysis (convergence, order of
consistency, etc. ) being presented, their proofs are not provided.
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