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Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field

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Abstract

In this paper we consider the issue of sliding motion in Filippov systems on the intersection of two or more surfaces. To this end, we propose an extension of the Filippov sliding vector field on manifolds of co-dimension p, with p ≥ 2. Our model passes through the use of a multivalued sign function reformulation. To justify our proposal, we will restrict to cases where the sliding manifold is attractive. For the case of co-dimension p = 2, we will distinguish between two types of attractive sliding manifold: “node-like” and “spiral-like”. The case of node-like attractive manifold will be further extended to the case of p ≥ 3. Finally, we compare our model to other existing methodologies on some examples.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Luca Dieci

  2. Dip. di Matematica, Universitá di Bari, Via Orabona 4, 70125, Bari, Italy

    Luciano Lopez

Authors
  1. Luca Dieci
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  2. Luciano Lopez
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Correspondence to Luciano Lopez.

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Dieci, L., Lopez, L. Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field. Numer. Math. 117, 779–811 (2011). https://doi.org/10.1007/s00211-011-0365-4

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