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Elsevier, Journal of Differential Equations, 4(254), p. 1800-1832, 2013

DOI: 10.1016/j.jde.2012.11.007

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A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis

Journal article published in 2013 by Luca Dieci, Cinzia Elia, Luciano Lopez ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

We consider sliding motion, in the sense of Filippov, on a discontinuity surface Σ of co-dimension 2. We characterize, and restrict to, the case of Σ being attractive through sliding. In this situation, we show that a certain Filippov sliding vector field fFfF (suggested in Alexander and Seidman, 1998 [2], di Bernardo et al., 2008 [6], Dieci and Lopez, 2011 [10]) exists and is unique. We also propose a characterization of first order exit conditions, clarify its relation to generic co-dimension 1 losses of attractivity for Σ, and examine what happens to the dynamics on Σ for the aforementioned vector field fFfF. Examples illustrate our results.