Hybrid automata extend finite state machines with real valued variables
that are subject to continuous evolutions (during time elapsing)
constrained by differential constraints and subject to discrete evolutions
(during mode switches) constrained by guards and updates. A large part
of the talk will target a general audience of researchers interested in the
modeling of systems ranging from embedded control systems to
biological systems. In a last part of the talk, I will present recent results
about the decidability frontier of the time-bounded reachability problem
for hybrid automata.