  In this brief paper we introduce a robust-safety notion for differential
inclusions, and we propose a general framework to certify such a notion in
terms of barrier functions. While existing literature studied only what we
designate by uniform robust safety, in this paper, we make a clear distinction
between the uniform and the non-uniform robust-safety notions. For both cases,
we establish sufficient (infinitesimal) conditions on the nominal (unperturbed)
system. That is, our conditions involve only the barrier function and the
system's right-hand side. Our results allow for unbounded safety regions as
well as nonsmooth barrier functions. Throughout the paper, simple examples are
provided to illustrate our results.
