  We propose an explicit, easily-computable algebraic criterion for approximate
null-controllability of a class of general piecewise linear switch systems with
multiplicative noise. This gives an answer to the general problem left open in
[13]. The proof relies on recent results in [4] allowing to reduce the dual
stochastic backward system to a family of ordinary differential equations.
Second, we prove by examples that the notion of approximate controllability is
strictly stronger than approximate null-controllability. A sufficient criterion
for this stronger notion is also provided. The results are illustrated on a
model derived from repressed bacterium operon (given in [19] and reduced in
[5]).
