  An example of a time-invariant time-delay system that is uniformly globally
attractive and exponentially stable, hence forward complete, but whose
reachability sets from bounded initial conditions are not bounded over compact
time intervals is provided. This gives a negative answer to two current
conjectures by showing that (i) forward completeness is not equivalent to
robust forward completeness (i.e. boundedness of reachability sets) and (ii)
global asymptotic stability is not equivalent to uniform global asymptotic
stability. In addition, a novel characterization of robust forward completeness
for systems having a finite number of discrete delays is provided. This
characterization relates robust forward completeness of the time-delay system
with the forward completeness of an associated nondelayed finite-dimensional
system.
