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

Abstract

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.

In Russian (English abstract), PostScript, 16 pages