Abstract
In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form
where \(g_1,g_2,\varphi :U\rightarrow \mathbb {R}\) are smooth functions and \(U\subseteq \mathbb {R}^2\) is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form
arise when the Sotomayor–Teixeira regularization is applied with \((x, y) \in U\) , \(\varepsilon \ge 0\), and f, g smooth in all variables.
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The authors are partially supported by CAPES, CNPq-Brazil, FAPESP and FP7-PEOPLE-2012-IRSES 318999.
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Lopes, B.D., da Silva, P.R. & Teixeira, M.A. Piecewise Implicit Differential Systems. J Dyn Diff Equat 29, 1519–1537 (2017). https://doi.org/10.1007/s10884-016-9538-2
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DOI: https://doi.org/10.1007/s10884-016-9538-2