On the new notion of input-to-state safety

In this paper, we study robustness analysis of systems' safety with respect to external input (or disturbance) signals. To this end, we introduce a new notion of input-to-state safety (ISSf) which allows us to quantify the systems' safety robustness, in the same way as the application of input-to-state stability (ISS) notion for analyzing robustness of systems' stability. In particular, ISSf prescribes the relationship between the evolution of state distance to the unsafe set with the initial conditions and the bounded external input signals. Finally, we discuss how to combine this notion with ISS for analyzing the robustness of both systems' stability and safety.