  This paper studies reachability and null-controllability for difference
inclusions involving convex processes. Such difference inclusions arise, for
instance, in the study of linear discrete-time systems whose inputs and/or
states are constrained to lie within a convex cone. After developing a
geometric framework for convex processes relying on invariance properties, we
provide necessary and sufficient conditions for both reachability and
null-controllability in terms of the spectrum of dual processes.
