A behavioral approach to positive interpolation
Antoulas, Athanasios C.
Master of Science thesis
We study interpolation by positive functions from a behavioural point of view. In particular, by considering the notion of mirror image data, the interpolation problem with passivity constraint is transformed into an unconstrained behavioural modeling one. It will be shown that the generating system for this problem has to be unitary with respect to an indefinite matrix. Using this approach, several results in the theory of interpolation by positive functions are derived in a very natural manner. The use of generating systems leads in a natural way to the recent results obtained by Byrnes et al concerning parametrizing the set of interpolants by the spectral zeros. We then apply the same approach to interpolation on the boundary.
Engineering, Electronics and Electrical