Sharp sufficient attractivity conditions for sliding on a co-dimension 2 discontinuity surface

We consider Filippov sliding motion on a co-dimension 2 discontinuity surface. We give conditions under which Σ is attractive through sliding which are sharper than those given in a previous paper of ours. Under these sharper conditions, we show that the sliding vector field considered in the same paper is still uniquely defined and varies smoothly in x ∈ Σ. A numerical example illustrates our results.