A hybrid automaton is a finite-state machine with a finite set of continuous variables whose values are described by a set of ordinary differential equations.
This combined specification of discrete and continuous behaviors enables dynamic systems that comprise both digital and analog components to be modeled and analyzed.
A simple example is a room-thermostat-heater system where the temperature of the room evolves according to laws of thermodynamics and the state of the heater (on/off); the thermostat senses the temperature, performs certain computations and turns the heater on and off.
In fact, a straightforward reduction from counter machines to three variables hybrid automata (two variables for storing counter values and one to restrict spending a unit-time per location) proves the undecidability of the reachability problem for hybrid automata.
Other notable decidable subclasses include initialized rectangular hybrid automata,[3] one-dimensional piecewise-constant derivatives (PCD) systems,[4] priced timed automata,[5] and constant-rate multi-mode systems.