Sufficient conditions for forward invariance and contractivity in hybrid inclusions using barrier functions

This paper studies set invariance and contractivity in hybrid systems modeled by inclusions using barrier functions. After introducing the notion of function, we investigate sufficient conditions to guarantee different forward notions a closed for with nonuniqueness solutions terminating prematurely. We consider (pre-)invariance sets, which guarantees that maximal starting from stay it, (pre-)contractivity, further requires boundary evolve immediately (continuously or discretely) towards its interior. Our are infinitesimal terms proposed Examples illustrate results.