Opuscula Math. 40, no. 6 (2020), 685-702

Opuscula Mathematica

A note on attractivity for the intersection of two discontinuity manifolds

Fabio V. Difonzo

Abstract. In piecewise smooth dynamical systems, a co-dimension 2 discontinuity manifold can be attractive either through partial sliding or by spiraling. In this work we prove that both attractivity regimes can be analyzed by means of the moments solution, a spiraling bifurcation parameter and a novel attractivity parameter, which changes sign when attractivity switches from sliding to spiraling attractivity or vice-versa. We also study what happens at what we call attractivity transition points, showing that the spiraling bifurcation parameter is always zero at those points.

Keywords: piecewise smooth systems, sliding motion, co-dimension 2, discontinuity manifold, attractivity.

Mathematics Subject Classification: 34A36.

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  • Fabio V. Difonzo
  • ORCID iD https://orcid.org/0000-0003-0101-3391
  • Czech Technical University in Prague, Department of Computer Science, Faculty of Electrical Engineering, Karlovo nám. 13, 120 00 Nové Město, Prague, Czech Republic
  • Code Architects Srl, Via Campania 1, 70029 Santeramo in Colle (BA), Italy
  • Communicated by Paweł Przybyłowicz.
  • Received: 2020-09-18.
  • Revised: 2020-10-03.
  • Accepted: 2020-10-05.
  • Published online: 2020-12-01.
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Cite this article as:
Fabio V. Difonzo, A note on attractivity for the intersection of two discontinuity manifolds, Opuscula Math. 40, no. 6 (2020), 685-702, https://doi.org/10.7494/OpMath.2020.40.6.685

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