  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.
