Minimal covariance realization and system identification algorithm for a class of stochastic linear switched systems with i.i.d. switching

In this paper, we consider stochastic realization theory of Linear Switched Systems (LSS) with i.i.d. switching. We characterize minimality of stochastic LSSs and show existence and uniqueness (up to isomorphism) of minimal LSSs in innovation form. We present a realization algorithm to compute a minimal LSS in innovation form from output and input covariances. Finally, based on this realization algorithm, by replacing true covariances with empirical ones, we propose a statistically consistent system identification algorithm.