Convex combinations are used to express a point in a set as a weighted sum of the extreme points of this set. Therefore, convex combinations are used in many different applications, including control. When controlling linear parameter varying systems which are affected by disturbances, there exist robust control algorithms [1] which use convex combinations to interpolate between extreme control...

In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the conv...

A positively convex module is a non-empty set closed under positively convex combinations but not necessarily a subset of a linear space. Positively convex modules are a natural generalization of positively convex subsets of linear spaces. Any positively convex module has a canonical semimetric and there is a universal positively affine mapping into a regularly ordered normed linear space and a...