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In this brief paper we introduce a robust-safety notion for differentialinclusions, and we propose a general framework to certify such a notion interms of barrier functions. While existing literature studied only what wedesignate by uniform robust safety, in this paper, we make a clear distinctionbetween 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 thesystem's right-hand side. Our results allow for unbounded safety regions aswell as nonsmooth barrier functions. Throughout the paper, simple examples areprovided to illustrate our results.

Sufficient Conditions for Robust Safety in Differential Inclusions Using Barrier Functions