On eigenvectors of convex processes in non-pointed cones

TL;DR

This paper generalizes spectral analysis of convex processes to non-pointed cones, extending eigenvalue characterizations and linking them to classical geometric control theory.

Contribution

It extends existing eigenvalue characterizations of convex processes from pointed to non-pointed cones, broadening the theoretical framework.

Findings

Generalization of eigenvalue characterization to non-pointed cones

Connection established between convex process analysis and geometric control theory

Enhanced understanding of controllability and stabilizability in broader cone settings

Abstract

Spectral analysis of convex processes has led to many results in the analysis of differential inclusions with a convex process. In particular the characterization of eigenvalues with eigenvectors in a given cone has led to results on controllability and stabilizability. However, these characterizations can handle only pointed cones. This paper will generalize all known results characterizing eigenvalues of convex processes with eigenvectors in a given cone. In addition, we reveal the link between the assumptions on our main theorem and classical geometric control theory.