Cascade Connection of Multiparametric Linear Systems and a Conservative Realization of Decomposable Inner Operator Functions in Bidisk

We introduce the notion of cascade connection of multiparametric discrete time-invariant linear dynamical systems with unit delay. This allows us to construct the explicit example of conservative realization of a decomposable operator-valued function $\theta (z_1, z_2)=\theta_2(z_2)\theta_1(z_1)$, where $\theta_1$ and $\theta_2$ are inner operator-valued functions on the unit disk, vanishing at zero, and discuss some properties of such realization.