A Fast Passivity Test for Stable Descriptor Systems via Skew-Hamiltonian/Hamiltonian Matrix Pencil Transformations

Passivity of a linear system is an important property to guarantee stable global simulation. Most circuits and interconnected systems are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their regular (nonsingular) state space counterparts. For large-scale DSs, the existing linear-matrix-inequality test is computationally prohibitive. Other system decoupling techniques involve complicated algorithms and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the insight that the sum of a passive system and its adjoint must render an impulse-free system under minimal realization. The proper part (nonimpulsive part) and the residue matrix at infinity (impulsive part), if any, of a passive DS are conveniently extracted using numerically efficient skew-Hamiltonian/Hamiltonian matrix pencil techniques. Numerical experiments confirm the effectiveness of the proposed test over conventional approaches.