Barrier Functions for Robust Safety in Differential Inclusions, Part I: Sufficient Conditions

This work proposes a general framework to analyze robust safety for continuous-time systems described by differential inclusions. While the existing robust-safety 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, involving only the barrier function and the system’s right-hand side. Our results allow for unbounded safety regions as well as non-smooth barrier functions. Throughout the paper, simple examples are provided to motivate the main results.