Stochastic realization with exogenous inputs and 'subspace-methods' identification

In this paper we study stochastic realization of stationary processes with exogenous inputs in the absence of feedback and we briefly discuss its application to identification. In particular, we derive and characterize the family of minimal state-space models of such processes and introduce a very natural block structure which is generically minimal. This model structure leads very naturally to 'subspace'-based identification algorithms which have a simpler structure of those existing in the literature.