Passivity preserving model reduction via interpolation of spectral zeros

An algorithm is developed for passivity preserving model reduction of LTI systems. The derivation is justified analytically and implementation schemes are developed for both medium scale (dense) and large scale (sparse) applications. The algorithm is based upon interpolation of specified spectral zeros of the original transfer function to produce a reduced transfer function that has the specified roots as its spectral zeros. These interpolation conditions are satisfied through the computation of a basis for a selected invariant subspace of a certain blocked matrix which has the spectral zeros as its spectrum.