Passivity preserving model reduction via interpolation of spectral zeros: Selection criteria and implementation
Nong, Hung Dinh
Sorensen, Danny C.
Master of Arts
This thesis presents spectral zero selection criteria for a rigorous theory on passivity preserving model reduction via interpolation of spectral zeros. For linear time invariant systems in circuit simulation, passivity implies stability, and hence need be preserved during model reduction. Sorensen  presents an algorithm that constructs passive reduced models which are much less expensive to simulate than the originals. The algorithm transforms the model reduction problem into a highly-structured generalized eigenvalue problem whose generalized eigenvalues are the spectral zeros of the original model. The reduced models constructed by interpolating the spectral zeros are passive and hence stable. This thesis first introduces spectral zero selection criteria for which the reduced model resulting from interpolation is a good approximation to the original. The physical interpretation for the criteria is presented. Second, by modifying the selection criteria, an algorithm of two-stage reduction is formulated to handle large-scale systems.
Mathematics; Electrical engineering; Applied sciences; Pure sciences