  In the discrete modeling approach for hybrid control systems, the continuous
plant is reduced to a discrete event approximation, called the DES-plant, that
is governed by a discrete event system, representing the controller. The
observability of the DES-plant model is crucial for the synthesis of the
controller and for the proper closed loop evolution of the hybrid control
system. Based on a version of the framework for hybrid control systems proposed
by Antsaklis, the paper analysis the relation between the properties of the
cellular space of the continuous plant and a mechanism of plant-symbols
generation, on one side, and the observability of the DES-plant automaton on
the other side. Finally an observable discrete event abstraction of the
continuous double integrator is presented.
