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  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.
Uitgever: Taylor & Francis
Bronbestand: Elektronische Wetenschappelijke Tijdschriften
 
 

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