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 θ (z1, z2)=θ2(z2)θ1(z1), where θ1 and θ2 are inner operator-valued functions on the unit disk, vanishing at zero, and discuss some properties of such realization.
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