The Structure of Inner Matrices that Satisfy Multiple Directional Interpolation Requirements

The structure of an inner matrix that satisfies directional interpolation requirements for nondistinct values at the right half-plane is derived explicitly, in closed form, in terms of the interpolation directions. The simple expression that is obtained for the required inner transfer function matrix has the same structure as the one that has already been found for distinct interpolation requirements, and it thus provides a comprehensive treatment, in the frequency domain, of interpolation problems that arise in many areas of linear system optimization.