Abstract
This chapter provides a mathematical theory applicable to the study of second-order dynamic systems with unilateral contact and friction. Conditions ensuring stability (in the sense of Lyapunov), attractivity, and asmptotic stability are given. Some illustrative small-sized examples in unilateral mechanics and in nonregular electrical circuits are also presented. Finally, a rigorous mathematical stability analysis of a DC-DC Buck converter is presented by using tools from nonsmooth and variational analysis.
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Notes
- 1.
Where \(\overline{ \mathbb {B}}_m(0,\gamma )\) denotes the closed ball of center 0 and radius \(\gamma \) in \({\mathbb {R}}^m\).
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Adly, S. (2017). Stability Analysis of Second-Order Nonsmooth Dynamics. In: A Variational Approach to Nonsmooth Dynamics. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-68658-5_4
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DOI: https://doi.org/10.1007/978-3-319-68658-5_4
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68657-8
Online ISBN: 978-3-319-68658-5
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