On the Inverse of Some Sign Matrices and on the Moments Sliding Vector Field on the Intersection of Several Manifolds: Nodally Attractive Case

In this paper, we consider selection of a sliding vector field of Filippov type on a discontinuity manifold Σ of co-dimension 3 (intersection of three co-dimension 1 manifolds). We propose an extension of the moments vector field to this case, and—under the assumption that Σ is nodally attractive—we prove that our extension delivers a uniquely defined Filippov vector field. As it turns out, the justification of our proposed extension requires establishing invertibility of certain sign matrices. Finally, we also propose the extension of the moments vector field to discontinuity manifolds of co-dimension 4 and higher.