On Invariants for Open Hybrid Systems and their Interconnections

For a broad class of hybrid dynamical systems with inputs, termed open hybrid inclusions, a general inter-connection model and solution concept are introduced. This model is employed to certify forward invariance of a set for the interconnection. The forward invariance notion allows for Zeno solutions and solutions that end prematurely – namely, maximal solutions that are not complete. Sufficient conditions for forward invariance of a set that are compositional and involve a properly defined scalar-valued barrier function are proposed. An example illustrates the ideas.