A Behavioural Approach to Positive Real Interpolation

Abstract

We study interpolation by positive real 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. The main conclusion is that the generating system for this problem has to be unitary with respect to an indefinite matrix. In addition we investigate the multiple-point positive real interpolation problem. This leads to a solution of the positive real realization problem where the data are Markov parameters.