UC Santa Cruz

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