Boundary results for positively invariant cones and their reachability cones
Titel:
Boundary results for positively invariant cones and their reachability cones
Auteur:
Neumann, Michael Stern, Ronald J.
Verschenen in:
Linear & multilinear algebra
Paginering:
Jaargang 17 (1985) nr. 2 pagina's 143-154
Jaar:
1985-04
Inhoud:
We say that a closed, convex, and solid cone [image omitted] is positively invariant with respect to the linear system of differential equations [image omitted] . In a previous paper, [2], the authors obtained formulas for the closure of the reachability cone [image omitted] under certain additional assumptions on A. The purpose of the present paper is to characterize the set XA(K) x∩ ∂ XA(K) which consists of those points on the boundary of XA(K) which actually reach A, in the case when K is a simplicial cone. We use this characterization to construct an algorithm for the computation of XA(K) from its closure. Furthermore, to obtain our characterization we develop a result which is of interest in itself, namely, that the maximal positively invariant subset of the boundary of a positively invariant simplicial cone k is, precisely, the union of its positively invariant faces.