Interpolation and feedback in a behavioral approach

We explore the connection between rational interpolation and partial realization. It is well known that partial realization is a special case of rational interpolation. In this paper, we present the converse result: any minimal rational interpolation problem can be reformulated as a minimal partial realization problem. As a result, solution methods for minimal partial realization can be used for minimal rational interpolation. Previously, the minimal partial realization problem has been formulated in a behavioral setting. This has led to a system-theoretic explanation of one of its most efficient solution methods: the Berlekamp-Massey algorithm. We show that this algorithm can also be used for interpolation purposes