Sufficient conditions for robust safety in differential inclusions using barrier functions

This paper considers robust-safety notions for differential inclusions. A general framework is proposed to certify the considered notions in terms of barrier functions. While most existing literature has focused solely on what we designate as uniform robust safety, in this paper, we make a clear distinction between uniform and non-uniform robust safety. For both cases, we establish sufficient conditions on the nominal (unperturbed) system. Our conditions involve 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. The paper concludes with applications to safety-critical self-triggered control and fast-slow dynamics as well as assume–guarantee contracts.