  We study a notion of convex cocompactness for discrete subgroups of the
projective general linear group acting (not necessarily irreducibly) on real
projective space, and give various characterizations. A convex cocompact group
in this sense need not be word hyperbolic, but we show that it still has some
of the good properties of classical convex cocompact subgroups in rank-one Lie
groups. Extending our earlier work arXiv:1701.09136 from the context of
projective orthogonal groups, we show that for word hyperbolic groups
preserving a properly convex open set in projective space, the above general
notion of convex cocompactness is equivalent to a stronger convex cocompactness
condition studied by Crampon-Marquis, and also to the condition that the
natural inclusion be a projective Anosov representation. We investigate
examples.
