  This paper studies system theoretic properties of the class of difference
inclusions of convex processes. We will develop a framework considering
eigenvalues and eigenvectors, weakly and strongly invariant cones, and a
decomposition of convex processes. This will allow us to characterize
reachability, stabilizability and (null-)controllability of nonstrict convex
processes in terms of spectral properties. These characterizations generalize
all previously known results regarding for instance linear processes and
specific classes of nonstrict convex processes.
