GHM: A generalized Hamiltonian method for passivity test of impedance/admittance descriptor systems

A generalized Hamiltonian method (GHM) is proposed for passivity test of descriptor systems (DSs) which describe impedance or admittance input-output responses. GHM can test passivity of DSs with any system index without minimal realization. This frequency-independent method can avoid the time-consuming system decomposition as required in many existing DS passivity test approaches. Furthermore, GHM can test systems with singular D + DT where traditional Hamiltonian method fails, and enjoys a more accurate passivity violation identification compared to frequency sweeping techniques. Numerical results have verified the effectiveness of GHM. The proposed method constitutes a versatile tool to speed up passivity check and enforcement of DSs and subsequently ensures globally stable simulations of electrical circuits and components.

[1]  James Demmel,et al.  The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I: theory and algorithms , 1993, TOMS.

[2]  Stefano Grivet-Talocia,et al.  Passivity enforcement via perturbation of Hamiltonian matrices , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Ngai Wong,et al.  Fast sweeping methods for checking passivity of descriptor systems , 2008, APCCAS 2008 - 2008 IEEE Asia Pacific Conference on Circuits and Systems.

[4]  Roswitha März,et al.  Canonical projectors for linear differential algebraic equations , 1996 .

[5]  Roland W. Freund,et al.  Reduced-Order Modeling of Large Linear Subcircuits via a Block Lanczos Algorithm , 1995, 32nd Design Automation Conference.

[6]  Leee/acm International Conference On Computer-aided Design Digest Of Technical Papers , 1993, Proceedings of 1993 International Conference on Computer Aided Design (ICCAD).

[7]  Zhaojun Bai,et al.  Eigenvalue-based characterization and test for positive realness of scalar transfer functions , 2000, IEEE Trans. Autom. Control..

[8]  Sheldon X.-D. Tan,et al.  Passive Modeling of Interconnects by Waveform Shaping , 2007, 8th International Symposium on Quality Electronic Design (ISQED'07).

[9]  Tatjana Stykel,et al.  Gramian-Based Model Reduction for Descriptor Systems , 2004, Math. Control. Signals Syst..

[10]  Ngai Wong,et al.  A Fast Passivity Test for Stable Descriptor Systems via Skew-Hamiltonian/Hamiltonian Matrix Pencil Transformations , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

[12]  Luís Miguel Silveira,et al.  Guaranteed passive balancing transformations for model order reduction , 2002, DAC '02.

[13]  Roland W. Freund,et al.  An extension of the positive real lemma to descriptor systems , 2004, Optim. Methods Softw..

[14]  Ronald A. Rohrer,et al.  Three dimensional circuit oriented electromagnetic modeling for VLSI interconnects , 1992, Proceedings 1992 IEEE International Conference on Computer Design: VLSI in Computers & Processors.

[15]  James Demmel,et al.  The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II: software and applications , 1993, TOMS.

[16]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[17]  Gene H. Golub,et al.  Matrix computations , 1983 .