Multivariate extensions are presented of results obtained in 1985 on the identification of univariate linear systems with noise and stationary inputs. It is noteworthy that this generalization is not straightforward; in fact the non-commutativity of matrix polynomials plays a role, a complication which was also encountered in deriving informative sample sizes for multivariate ARMA processes. Results are derived for the case of a d-variate linear system with an m-variate ARMA input process. The results are presented as informative sampling schemes, i.e. finite time intervals for input and output processes such that observation of the system during these time periods guarantees global identifiability of the system.