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This paper studies set invariance and contractivity in hybrid systems modeledby hybrid inclusions using barrier functions. After introducing the notion of amultiple barrier functions, we investigate the tightest possible sufficientconditions to guarantee different forward invariance and contractivity notionsof a closed set for hybrid systems with nonuniqueness of solutions andsolutions terminating prematurely. More precisely, we consider forward(pre-)invariance of sets, which guarantees solutions to stay in a set, and(pre-)contractivity, which further requires solutions that reach the boundaryof the set to evolve (continuously or discretely) towards its interior. Ourconditions for forward invariance and contractivity involve infinitesimalconditions in terms of multiple barrier functions. Examples illustrate theresults. Keywords: Forward invariance, contractivity, barrier functions, hybriddynamical systems.

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