  We study a class of systems whose parameters are driven by a Markov chain in
reverse time. A recursive characterization for the second moment matrix, a
spectral radius test for mean square stability and the formulas for optimal
control are given. Our results are determining for the question: is it possible
to extend the classical duality between filtering and control of linear systems
(whose matrices are transposed in the dual problem) by simply adding the jump
variable of a Markov jump linear system. The answer is positive provided the
jump process is reversed in time.
