A Global Analysis Approach to Passivity Preserving Model Reduction

Passivity-preserving model reduction for linear time-invariant systems amounts to approximating a positive-real rational transfer function with one of lower degree. Antoulas and Sorensen have proposed such a model-reduction method based on Krylov projections. The method is based on an observation by Antoulas (in the single-input/single-output case) that if the approximant is preserving a subset of the spectral zeros and takes the same values as the original transfer function in the mirror points of the preserved spectral zeros, then the approximant is also positive real. However, this turns out to be a special solution in the theory of analytic interpolation with degree constraint developed by Byrnes et al. (2001), namely the maximum-entropy (central) solution. By tuning the interpolation points and the spectral zeros, as prescribed by this theory, one is able to obtain considerably better reduced-order models