  We aim at characterizing viability, invariance and some reachability
properties of controlled piecewise deterministic Markov processes (PDMPs).
Using analytical methods from the theory of viscosity solutions, we establish
criteria for viability and invariance in terms of the first order normal cone.
We also investigate reachability of arbitrary open sets. The method is based on
viscosity techniques and duality for some associated linearized problem. The
theoretical results are applied to general On/Off systems, Cook's model for
haploinssuficiency, and a stochastic model for bacteriophage lambda.
