A geometric approach to convex processes: from reachability to stabilizability

Abstract

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.