On the inverse of some sign matrices and on the Moments sliding vector field on the intersection of several manifolds: nodally attractive case

Series: 
SIAM Student Seminar
Friday, October 23, 2015 - 14:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Institute of Technology
In this paper, we consider selection of a sliding vector fieldof Filippov type on a discontinuity manifold $\Sigma$ 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 $\Sigma$ is nodally attractive -we prove that our extension delivers a uniquely definedFilippov vector field. As it turns out, the justification of our proposed extension requiresestablishing invertibility of certain sign matrices.  Finally,we also propose the extension of the moments vector field todiscontinuity manifolds of co-dimension 4 and higher.