A geometric approach to convex processes: from reachability to stabilizability

TL;DR

This paper introduces a geometric framework for analyzing convex process systems, providing spectral characterizations of reachability and stabilizability that extend known results from linear and specific convex processes.

Contribution

It develops a spectral-based geometric approach to characterize key properties of convex processes, generalizing previous results for linear and particular convex systems.

Findings

Spectral conditions for reachability and stabilizability of convex processes

Decomposition of convex processes into eigencomponents

Unified framework extending classical linear system results

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.