Realization theory of stochastic jump-Markov linear systems

We present a stochastic realization theory for stochastic jump-Markov linear systems (JMLSs). We derive necessary and sufficient conditions for existence of a realization, along with a characterization of minimality in terms of reachability and observability. We also sketch a realization algorithm and argue that minimality can be checked algorithmically. The main tool for solving the stochastic realization problem for JMLSs is the formulation and solution of a stochastic realization problem for a general class of bilinear systems with nonwhite-noise inputs using the theory of formal power series.