Guaranteed stable projection-based model reduction for indefinite and unstable linear systems

IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD

Volumn , Issue , 2008, Pages 728-735

  Bond, Bradley N ^a   Daniel, Luca ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

A STABILITIES; A STABLES; ANALOG APPLICATIONS; BALANCED TRUNCATIONS; EXISTING METHODS; INDEFINITE SYSTEMS; LARGE SYSTEMS; LINEAR CONSTRAINTS; MATCHING METHODS; MODEL REDUCTIONS; OPTIMIZATION PROBLEMS; ORIGINAL SYSTEMS; POWER DISTRIBUTION GRIDS; PROJECTION MATRIXES; REDUCED MODELS; REDUCTION TECHNIQUES; RF INDUCTORS; STANDARD MODELS; UNSTABLE LINEAR SYSTEMS;

ANALOG CIRCUITS; APPLICATIONS; COMPUTATIONAL COMPLEXITY; COMPUTER AIDED DESIGN; DIGITAL CIRCUITS; DIGITAL DEVICES; DIGITAL INTEGRATED CIRCUITS; INTEGRATED CIRCUITS; LINEAR SYSTEMS; MATHEMATICAL MODELS; METHOD OF MOMENTS; VLSI CIRCUITS;

SYSTEM STABILITY;

EID: 57849105429     PISSN: 10923152     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ICCAD.2008.4681657     Document Type: Conference Paper

References (24)

1. Eric Grimme. Krylov Projection Methods for Model Reduction. PhD thesis, Coordinated-Science Laboratory, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, 1997.
2. Zhaojun Bai, Peter Feldmann, and Roland W. Freund, Stable and passive reduced order models based on partial pade approximation via the lanczos process. Technical Report Numerical Analysis Manuscript No.97-3-10. Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey, October 1997.
3. A. Odabasioglu, M. Celik, and L. T. Pileggi. PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems. 17(8):645-654, August 1998.
4. K. J. Kerns, I. L. Wemple, and A. T. Yang. Stable and efficient reduction of substrate model networks using congruence transforms. In Proc. of the IEEE/ACM International Conference on Computer-Aided Design, pages 207 - 214, San Jose, CA, November 1995.
5. L. M. Silveira, M. Kamon, I. Elfadel, and J. K. White. Coordinate-transformed arnoldi algorithm for generating guarantee stable reduced-order models of RLC. Computer Methods in Applied Mechanics and Engineering, 169(3-4):377-89, February 1999.
6. Freund. Krylov-subspace methods for reduced-order modeling in circuit simulation. In J. Comput. Appl. Math. volume 123, pages 395-421, 2000.
7. B. Bond and L. Daniel. Stabilizing schemes for piecewise-linear reduced order models via projection and weighting functions. In Proc. of the IEEE/ACM International Conference on Computer-Aided Design, San Jose, CA, 2007.
8. Bruce Moore. Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction. IEEE Transactions on Automatic Control, AC-26(1): 17-32, February 1981.
9. J. R. Phillips, L. Daniel, and M. Silveira. Guaranteed passive balancing transformations for model order reduction. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, 22(8): 1027-41, Aug 2003.
10. M. Vidyagasar. Nonlinear Systems Analysis. Prentice Hall. New York, 1978.
11. S. Sastry. Nonlinear Systems: Analysis, Stability, and Control. Springer, New York, 1999.
12. T. Stykel. Stability and inertia theorems for generalized lyapunov equations. Linear Algebra and its Applications, volume=.
13. J. C. Willems. Dissipative dynamical systems. Arch. Rational Mechanics and Analysis. 45:321-393, 1972.
14. Anders Rantzer. On the Kalman-Yakubovich-Popov lemma. Systems and Control Letters, 27(5), January 1996.
15. R. Freund and F. Jarre. An extension of the positive real lemma to descriptor systems. Technical Report Numerical Analysis Manuscript No.00-3-09. Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey, December 2000.
16. P. Feldmann and R. W. Freund. Efficient linear circuit analysis by Padé approximation via the Lanczos process. In Proceedings of EURO-DAC '94 with EURO-VHDL '94, Grenoble, France, pages 170-175. IEEE Computer Society Press, 1994.
17. R. W. Freund and P. Feldmann. The SyMPVL algorithm and its applications to interconnect simulation. In Proceedings of the 1997 International Conference on Simulation of Semiconductor Processes and Devices, pages 113-116. IEEE, 1997.
18. K. Willcox and J. Peraire. Balanced model reduction via the proper orthogonal decomposition. In Proceedings of the 15th AIAA Computational Fluid Dynamics Conference, Anaheim, CA, June 2001.
19. Joel Phillips and L. Miguel Silveira. Poor man's tbr: A simple model reduction scheme. In DATE '04: Proceedings of the conference on Design, automation and test in Europe, page 20938, Washington, DC, USA, 2004. IEEE Computer Society.
20. J.F. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12:625-653, 1999.
21. J. Lfberg. Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
22. Tarek Moselhy, Xin Hu, and Luca Daniel, pfft in fastmaxwell: a fast impedance extraction solver for 3d conductor structures over substrate. In DATE '07: Proceedings of the conference on Design, automation and test in Europe, pages 1194-1199. San Jose, CA, USA, 2007. EDA Consortium.
23. Fastmaxwell. http://www.rle.mit.edu/cpg/fastmaxwell.
24. S.D. Senturla E. Hung, Y.-J. Yahg. Low-order models for fast dynamical simulation of mems microstructures. In Proceedings of IEEE International Conference on Solid State Sensors and Actuators, volume 2, pages 1101-1104, 1997.