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

In this paper, we work with Linear Switched Systems (LSS). We show the existence of minimality in innovation form for such systems. We also present a realization algorithm to compute a minimal LSS in innovation form, by calculating the covariances of the state-pace matrices. Finally, a system identification algorithm statically consistent is presented. The later, based on the realization algorithm, uses the collected data in order to compute the covariances of the inputs and outputs.