  Consider the random process (Xt) solution of dXt/dt = A(It) Xt where (It) is
a Markov process on {0,1} and A0 and A1 are real Hurwitz matrices on R2.
Assuming that there exists lambda in (0, 1) such that (1 - \lambda)A0 +
\lambdaA1 has a positive eigenvalue, we establish that the norm of Xt may
converge to 0 or infinity, depending on the the jump rate of the process I. An
application to product of random matrices is studied. This paper can be viewed
as a probabilistic counterpart of the paper "A note on stability conditions for
planar switched systems" by Balde, Boscain and Mason.
