  We define a special class of hybrid automata, called Deterministic and
Transversal Linear Hybrid Automata (DTLHA), whose continuous dynamics in each
location are linear time-invariant (LTI) with a constant input, and for which
every discrete transition up to a given bounded time is deterministic and,
importantly, transversal. For such a DTLHA starting from an initial state, we
show that it is possible to compute an approximation of the reach set of a
DTLHA over a finite time interval that is arbitrarily close to the exact reach
set, called a bounded epsilon-reach set, through sampling and polyhedral
over-approximation of sampled states. We propose an algorithm and an attendant
architecture for the overall bounded epsilon-reach set computation process.
