  In this short note we prove a hierarchical stability result that applies to
hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et
al., 2012). In particular, we establish sufficient conditions for uniform
asymptotic stability of a compact set based on some hierarchical stability
assumptions involving two nested closed sets containing such a compact set.
Moreover, mimicking the well known result for cascaded systems, we prove that
the basin of attraction of such compact set coincides with the largest set from
which all solutions are bounded. The result appears to be useful when applied
to several recent works involving hierarchical control architectures.
