A fast passivity test for descriptor systems via structure-preserving transformations of skew-Hamiltonian/Hamiltonian matrix pencils

Passivity in a VLSI model is an important property to guarantee stable global simulation. Most VLSI models are naturally described as descriptor systems (DSs) or singular state spaces. Passivity tests for DSs, however, are much less developed compared to their non-singular state space counterparts. For large-scale DSs, the existing test based on linear matrix inequality (LMI) is computationally prohibitive. Other system decoupling techniques involve complicated coding and sometimes ill-conditioned transformations. This paper proposes a simple DS passivity test based on the key insight that the sum of a passive system and its adjoint must be impulse-free. A sidetrack shows that the proper (non-impulsive) part of a passive DS can be easily decoupled along the test flow. Numerical examples confirm the effectiveness of the proposed DS passivity test over conventional approaches.