A Variational Approach to Nonsmooth Dynamics

Applications in Unilateral Mechanics and Electronics

  • Samir Adly

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Samir Adly
    Pages 1-37
  3. Samir Adly
    Pages 39-51
  4. Samir Adly
    Pages 103-126
  5. Samir Adly
    Pages 127-148
  6. Back Matter
    Pages 149-159

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.


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

Authors and affiliations

  • Samir Adly
    • 1
  1. 1.Laboratoire XLIMUniversité de LimogesLimogesFrance

Bibliographic information