Determining the discriminating domain for hybrid linear differential game with two players and two targets

This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron.