  We construct a planar process that switches randomly between the flows of two
linear systems built from two Hurwitz matrices (all eigenvalues have negative
real parts). The goal here is to study the long time behaviour according to the
switching rates. We will see that, even if the two systems are stable, it is
possible to obtain a blow up if we choose the switching rates wisely. Finally
we will see a connection, between the tail of the invariant measure (when the
switching times follow an exponential law) and the existence of a deterministic
control that makes the process explode.
