A note on attractivity for the intersection of two discontinuity manifolds

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