  Recent results have shown the stability of frustration-free Hamiltonians to
weak local perturbations, assuming several conditions. In this paper, we prove
the stability of free fermion Hamiltonians which are gapped and local. These
free fermion Hamiltonians are not necessarily frustration-free, but we are able
to adapt previous work to prove stability. The key idea is to add an additional
copy of the system to cancel topological obstructions. We comment on
applications to quantization of Hall conductance in such systems.
