Poster on safety characterization in hybrid inclusions using barrier functions

By this poster, we aim at presenting in a comprehensive manner our new results on safety characterization using barrier functions in the general context of hybrid systems. Roughly speaking, a dynamical system is said to be safe when the solutions starting from a given initial set never reach a given unsafe set. Barrier functions in this context constitute a qualitative methodological tool that avoid the computation of the system's solutions yet to determine if the safety property holds. According to literature, a barrier function candidate with respect to a given initial and unsafe sets is nonpositive on the initial set and strictly positive on the unsafe set. Such a barrier candidate becomes a certificate of safety provided that it satisfies some variational properties involving the system's dynamics at least in a specific region around its zero-sublevel set