  The sequential compactness afforded hybrid systems under mild regularity
constraints guarantee outer/upper semicontinuous dependence of solutions on
initial conditions and perturbations. For reachable sets of hybrid systems,
this property leads to upper semicontinuous dependence with respect to initial
conditions, time, and perturbations. Motivated by these results, we define a
counterpart to sequential compactness and show that it leads to lower
semicontinuous dependence of solutions on initial conditions and perturbations.
In the sequel, it is shown that under appropriate assumptions, reachable sets
of systems possessing this novel property depend lower semicontinuously on
initial conditions, time, and perturbations. When those assumptions fail,
continuous approximations of reachable sets turn out to be still possible.
Necessary and sufficient conditions for the introduced property are given by a
combination of geometric constraints, regularity assumptions, and tangentiality
conditions. Further applications to simulations and optimal control of hybrid
systems are discussed.
