  This note explores reach set computations for perturbed delay differential
equations (DDEs). The perturbed DDEs of interest in this note is a class of
DDEs whose dynamics are subject to perturbations, and their solutions feature
the local homeomorphism property with respect to initial states. Membership in
this class of perturbed DDEs is determined by conducting sensitivity analysis
of solution mappings with respect to initial states to impose a bound
constraint on the time-lag term. The homeomorphism property of solutions to
such class of perturbed DDEs enables us to construct over- and
under-approximations of reach sets by performing reachability analysis on just
the boundaries of their permitted initial sets, thereby permitting an extension
of reach set computation methods for ordinary differential equations to
perturbed DDEs. Three examples demonstrate the performance of our approach.
