An efficient passivity test for descriptor systems via canonical projector techniques

An efficient passivity test based on matrix chain and canonical projector techniques is proposed for descriptor systems (DSs) commonly encountered in VLSI modeling. The test entails a natural flow that first evaluates the index of a DS, followed by possible decoupling into its proper and improper (if any) subsystems. Compared to the recent DS passivity tests using linear matrix inequality (LMI)-based extended positive real lemma or skew-Hamiltonian/ Hamiltonian (SHH) transformations, numerical examples show that the proposed projector approach is significantly more efficient. Explicit state space formulations for the decoupled subsystems that facilitate further processing such as passivity enforcement and model order reduction are also derived.