  The dynamics near a border-collision bifurcation are approximated to leading
order by a continuous, piecewise-linear map. The purpose of this paper is to
consider the higher-order terms that are neglected when forming this
approximation. For two-dimensional maps we establish conditions under which a
chaotic attractor created in a border-collision bifurcation persists for an
open interval of parameters beyond the bifurcation. We apply the results to a
prototypical power converter model to prove the model exhibits robust chaos.
