Overview
- Multidisciplinary and transversal to at least three communities: applied mathematicians, engineers and researchers in control theory and nonlinear systems
- Includes numerous examples, illustrations and applications to illustrate the theoretical mathematical results
- Highly accessible and self-contained
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (6 chapters)
Keywords
- nonsmooth dynamics
- Lyapunov stability
- stability analysis nonsmooth dynamics
- Moreau sweeping process
- nonsmooth mechanics
- evolution variational inequalities
- complementarity systems
- differential inclusions
- invariance principle
- unilateral dynamical systems
- nonregular electrical circuits
- DC-DC Buck converters
- Lur'e systems
- 34A60, 34H15, 37N40, 46N10, 47J22, 49J52
- 49J53, 65K10, 65K15, 90C33
About this book
This brief examines mathematical models in nonsmooth mechanics and nonregular electrical circuits, including evolution variational inequalities, complementarity systems, differential inclusions, second-order dynamics, Lur'e systems and Moreau's sweeping process.
The field of nonsmooth dynamics is of great interest to mathematicians, mechanicians, automatic controllers and engineers. The present volume acknowledges this transversality and provides a multidisciplinary view as it outlines fundamental results in nonsmooth dynamics and explains how to use them to study various problems in engineering. In particular, the author explores the question of how to redefine the notion of dynamical systems in light of modern variational and nonsmooth analysis.
With the aim of bridging between the communities of applied mathematicians, engineers and researchers in control theory and nonlinear systems, this brief outlines both relevant mathematical proofs and models in unilateral mechanics and electronics.
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Bibliographic Information
Book Title: A Variational Approach to Nonsmooth Dynamics
Book Subtitle: Applications in Unilateral Mechanics and Electronics
Authors: Samir Adly
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-68658-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s) 2017
Softcover ISBN: 978-3-319-68657-8Published: 20 March 2018
eBook ISBN: 978-3-319-68658-5Published: 19 February 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: XV, 159
Number of Illustrations: 29 b/w illustrations, 26 illustrations in colour
Topics: Calculus of Variations and Optimal Control; Optimization, Systems Theory, Control, Control and Systems Theory, Vibration, Dynamical Systems, Control, Applications of Graph Theory and Complex Networks