  We consider a family of singular maps as an example of a simple model of
dynamical systems exhibiting the property of robust chaos on a well defined
range of parameters. Critical boundaries separating the region of robust chaos
from the region where stable fixed points exist are calculated on the parameter
space of the system. It is shown that the transitions to robust chaos in these
systems occur either through the routes of type-I or type-III intermittency and
the critical boundaries for each type of transition have been determined on the
phase diagram of the system. The simplicity of these singular maps and the
robustness of their chaotic dynamics make them useful ingredients in the
construction of models and in applications that require reliable operation
under chaos.
