Fast and reliable passivity assessment and enforcement with extended Hamiltonian pencil

Passivity is an important property for a macro-model generated from measured or simulated data. Existence of purely imaginary eigenvalues of a Hamiltonian matrix provides useful information in assessing and correcting the passivity of a system. Since direct computation of eigenvalues is very expensive for large-scale systems, several authors have proposed to solve iteratively for a subset of the eigenvalues based on heuristic sampling along the imaginary axis. However, completeness is not guaranteed in such methods and thus potential risk of missing important eigenvalues is difficult to avoid. In this paper we are aiming at finding all eigenvalues efficiently to avoid both the high cost and the potential risk of missing important eigenvalues. The idea of the proposed method is to convert the Hamiltonian matrix to an equivalent sparse form, termed the “extended Hamiltonian pencil”, and solve for its eigenvalues efficiently using a special eigensolver. Experiments on several realistic systems demonstrate an 80X speed-up compared with standard direct eigensolvers.