Passivity test of immittance descriptor systems based on generalized Hamiltonian methods

Abstract—A generalized Hamiltonian method (GHM) and its half-size variant (HGHM) are proposed to characterize the spec-tral behaviors of descriptor systems (DSs). With the preprocess improper part test, GHM and HGHM can be applied to test the passivity of immittance (impedance or admittance) DSs without system decomposition, system index assumption, or minimal real-ization requirement, which are the major bottlenecks of existing algebraic DS passivity tests. The proposed method allows exact detection of nonpassive frequency intervals, which is not possible with frequency-sweeping techniques. Numerical results confirm the effectiveness of the proposed methods. Index Terms—Descriptor system (DS), generalized Hamiltonian method (GHM), half-size GHM (HGHM), passivity